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Update 2022-03-24 08:43

master
Jean-Sébastien 2 years ago
parent
1d852e7213
commit
50704eba07
100 changed files with 595 additions and 595 deletions
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build/a.html View File

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 <p class="author">Author: Jean-Sébastien Caux</p>
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 <p class="author">Author: Jean-Sébastien Caux</p>
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 <p class="author">Author: Jean-Sébastien Caux</p>
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-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
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 <p class="author">Author: Jean-Sébastien Caux</p>
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 <p class="author">Author: Jean-Sébastien Caux</p>
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 <p class="author">Author: Jean-Sébastien Caux</p>
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 <p class="author">Author: Jean-Sébastien Caux</p>
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build/c_m_cs.html View File

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-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
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build/c_m_cs_cyl.html View File

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   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
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   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
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   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
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   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
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 <a id="cyl_curl"></a><a href="./c_m_cs_cyl.html#cyl_curl"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
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1721 
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   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
1722 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
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   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
1723 
 </svg></a>
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 </svg></a>
1724 
 </p>
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 </p>
1725 
-<div class="alteqlabels" id="org8037114">
1725 
+<div class="alteqlabels" id="orga07a427">
1726 
 <ul class="org-ul">
 1726 
 <ul class="org-ul">
1727 
 <li>Gr4(2.21)</li>
 1727 
 <li>Gr4(2.21)</li>
1728 
 </ul>
 1728 
 </ul>
1771 
 </div>
 1771 
 </div>
1772 
 <div id="postamble" class="status">
 1772 
 <div id="postamble" class="status">
1773 
 <p class="author">Author: Jean-Sébastien Caux</p>
 1773 
 <p class="author">Author: Jean-Sébastien Caux</p>
1774 
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
1774 
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
1775 
 <p class="validation"></p>
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 <p class="validation"></p>
1776 
 </div>
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1777
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+ 3
- 3
build/c_m_cs_hyp.html View File

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2 
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 <meta name="viewport" content="width=device-width, initial-scale=1">
7 
 <title>Pre-Quantum Electrodynamics</title>
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 <title>Pre-Quantum Electrodynamics</title>
1293 
 </summary>
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 </summary>
1294 
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 <ul>
1295 
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1296 
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
1296 
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
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1299
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 </div>
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 </div>
1633 
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 <div id="postamble" class="status">
1634 
 <p class="author">Author: Jean-Sébastien Caux</p>
 1634 
 <p class="author">Author: Jean-Sébastien Caux</p>
1635 
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
1635 
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
1636 
 <p class="validation"></p>
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1637 
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build/c_m_cs_sph.html View File

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+<!-- 2022-03-24 Thu 08:42 -->
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 <meta name="viewport" content="width=device-width, initial-scale=1">
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 <meta name="viewport" content="width=device-width, initial-scale=1">
7 
 <title>Pre-Quantum Electrodynamics</title>
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 <title>Pre-Quantum Electrodynamics</title>
1293 
 </summary>
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 </summary>
1294 
 <ul>
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 <ul>
1295 
 <li>
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 <li>
1296 
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
1296 
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
1297
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 </li>
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 </li>
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1299
1623 
 The usual Cartesian coordinates relate to spherical coordinates
 1623 
 The usual Cartesian coordinates relate to spherical coordinates
1624 
 according to
 1624 
 according to
1625 
 </p>
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 </p>
1626 
-<div class="eqlabel" id="org309b2e9">
1626 
+<div class="eqlabel" id="org763df52">
1627 
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 <p>
1628 
 <a id="sph_xyz"></a><a href="./c_m_cs_sph.html#sph_xyz"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
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1629 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
 1629 
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1630 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 1630 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
1631 
 </svg></a>
 1631 
 </svg></a>
1632 
 </p>
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 </p>
1633 
-<div class="alteqlabels" id="org7a6a40a">
1633 
+<div class="alteqlabels" id="orgb59869b">
1634
1634
1635 
 </div>
 1635 
 </div>
1636
1636
1655 
 where the explicit relation between spherical and
 1655 
 where the explicit relation between spherical and
1656 
 Cartesian unit vectors is
 1656 
 Cartesian unit vectors is
1657 
 </p>
 1657 
 </p>
1658 
-<div class="eqlabel" id="org43b8824">
1658 
+<div class="eqlabel" id="org923fbbc">
1659 
 <p>
 1659 
 <p>
1660 
 <a id="sph_uv"></a><a href="./c_m_cs_sph.html#sph_uv"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
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1661 
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 1661 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
1662 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 1662 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
1663 
 </svg></a>
 1663 
 </svg></a>
1664 
 </p>
 1664 
 </p>
1665 
-<div class="alteqlabels" id="org054cde6">
1665 
+<div class="alteqlabels" id="org2051229">
1666
1666
1667 
 </div>
 1667 
 </div>
1668
1668
1685 
 <p>
 1685 
 <p>
1686 
 An infinitesimal displacement \(d{\bf l}\) can be written as
 1686 
 An infinitesimal displacement \(d{\bf l}\) can be written as
1687 
 </p>
 1687 
 </p>
1688 
-<div class="eqlabel" id="org0afd234">
1688 
+<div class="eqlabel" id="orgb032a0d">
1689 
 <p>
 1689 
 <p>
1690 
 <a id="sph_dl"></a><a href="./c_m_cs_sph.html#sph_dl"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
 1690 
 <a id="sph_dl"></a><a href="./c_m_cs_sph.html#sph_dl"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
1691 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
 1691 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
1692 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 1692 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
1693 
 </svg></a>
 1693 
 </svg></a>
1694 
 </p>
 1694 
 </p>
1695 
-<div class="alteqlabels" id="orgce4cca6">
1695 
+<div class="alteqlabels" id="orgaeea797">
1696
1696
1697 
 </div>
 1697 
 </div>
1698
1698
1708 
 <p>
 1708 
 <p>
1709 
 Infinitesimal volume element:
 1709 
 Infinitesimal volume element:
1710 
 </p>
 1710 
 </p>
1711 
-<div class="eqlabel" id="org260d3f6">
1711 
+<div class="eqlabel" id="orgf42297c">
1712 
 <p>
 1712 
 <p>
1713 
 <a id="sph_dtau"></a><a href="./c_m_cs_sph.html#sph_dtau"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
 1713 
 <a id="sph_dtau"></a><a href="./c_m_cs_sph.html#sph_dtau"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
1714 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
 1714 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
1715 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 1715 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
1716 
 </svg></a>
 1716 
 </svg></a>
1717 
 </p>
 1717 
 </p>
1718 
-<div class="alteqlabels" id="org5ac82f0">
1718 
+<div class="alteqlabels" id="orgb0160b3">
1719
1719
1720 
 </div>
 1720 
 </div>
1721
1721
1736 
 <div id="outline-container-c_m_cs_sph_grad" class="outline-6">
 1736 
 <div id="outline-container-c_m_cs_sph_grad" class="outline-6">
1737 
 <h6 id="c_m_cs_sph_grad"><a href="#c_m_cs_sph_grad">Gradient</a></h6>
 1737 
 <h6 id="c_m_cs_sph_grad"><a href="#c_m_cs_sph_grad">Gradient</a></h6>
1738 
 <div class="outline-text-6" id="text-c_m_cs_sph_grad">
 1738 
 <div class="outline-text-6" id="text-c_m_cs_sph_grad">
1739 
-<div class="eqlabel" id="org0a3cd9b">
1739 
+<div class="eqlabel" id="orgbf5f354">
1740 
 <p>
 1740 
 <p>
1741 
 <a id="sph_grad"></a><a href="./c_m_cs_sph.html#sph_grad"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
 1741 
 <a id="sph_grad"></a><a href="./c_m_cs_sph.html#sph_grad"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
1742 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
 1742 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
1743 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 1743 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
1744 
 </svg></a>
 1744 
 </svg></a>
1745 
 </p>
 1745 
 </p>
1746 
-<div class="alteqlabels" id="orgdf69aa8">
1746 
+<div class="alteqlabels" id="orgbda0409">
1747
1747
1748 
 </div>
 1748 
 </div>
1749
1749
1760 
 <div id="outline-container-c_m_cs_sph_div" class="outline-6">
 1760 
 <div id="outline-container-c_m_cs_sph_div" class="outline-6">
1761 
 <h6 id="c_m_cs_sph_div"><a href="#c_m_cs_sph_div">Divergence</a></h6>
 1761 
 <h6 id="c_m_cs_sph_div"><a href="#c_m_cs_sph_div">Divergence</a></h6>
1762 
 <div class="outline-text-6" id="text-c_m_cs_sph_div">
 1762 
 <div class="outline-text-6" id="text-c_m_cs_sph_div">
1763 
-<div class="eqlabel" id="orgc4833f8">
1763 
+<div class="eqlabel" id="orge3c6cf7">
1764 
 <p>
 1764 
 <p>
1765 
 <a id="sph_div"></a><a href="./c_m_cs_sph.html#sph_div"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
 1765 
 <a id="sph_div"></a><a href="./c_m_cs_sph.html#sph_div"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
1766 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
 1766 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
1767 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 1767 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
1768 
 </svg></a>
 1768 
 </svg></a>
1769 
 </p>
 1769 
 </p>
1770 
-<div class="alteqlabels" id="org12f3039">
1770 
+<div class="alteqlabels" id="orged88fee">
1771
1771
1772 
 </div>
 1772 
 </div>
1773
1773
1784 
 <div id="outline-container-c_m_cs_sph_curl" class="outline-6">
 1784 
 <div id="outline-container-c_m_cs_sph_curl" class="outline-6">
1785 
 <h6 id="c_m_cs_sph_curl"><a href="#c_m_cs_sph_curl">Curl</a></h6>
 1785 
 <h6 id="c_m_cs_sph_curl"><a href="#c_m_cs_sph_curl">Curl</a></h6>
1786 
 <div class="outline-text-6" id="text-c_m_cs_sph_curl">
 1786 
 <div class="outline-text-6" id="text-c_m_cs_sph_curl">
1787 
-<div class="eqlabel" id="org6a4b6db">
1787 
+<div class="eqlabel" id="org34ae3e4">
1788 
 <p>
 1788 
 <p>
1789 
 <a id="sph_curl"></a><a href="./c_m_cs_sph.html#sph_curl"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
 1789 
 <a id="sph_curl"></a><a href="./c_m_cs_sph.html#sph_curl"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
1790 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
 1790 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
1791 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 1791 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
1792 
 </svg></a>
 1792 
 </svg></a>
1793 
 </p>
 1793 
 </p>
1794 
-<div class="alteqlabels" id="org47ac74d">
1794 
+<div class="alteqlabels" id="org5f176f6">
1795
1795
1796 
 </div>
 1796 
 </div>
1797
1797
1810 
 <div id="outline-container-c_m_cs_sph_lap" class="outline-6">
 1810 
 <div id="outline-container-c_m_cs_sph_lap" class="outline-6">
1811 
 <h6 id="c_m_cs_sph_lap"><a href="#c_m_cs_sph_lap">Laplacian</a></h6>
 1811 
 <h6 id="c_m_cs_sph_lap"><a href="#c_m_cs_sph_lap">Laplacian</a></h6>
1812 
 <div class="outline-text-6" id="text-c_m_cs_sph_lap">
 1812 
 <div class="outline-text-6" id="text-c_m_cs_sph_lap">
1813 
-<div class="eqlabel" id="orgb7a43f7">
1813 
+<div class="eqlabel" id="orgb40c79b">
1814 
 <p>
 1814 
 <p>
1815 
 <a id="sph_Lap"></a><a href="./c_m_cs_sph.html#sph_Lap"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
 1815 
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1817 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
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   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
1818 
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1819 
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1820 
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 </div>
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 <div id="postamble" class="status">
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1853 
 <p class="author">Author: Jean-Sébastien Caux</p>
 1853 
 <p class="author">Author: Jean-Sébastien Caux</p>
1854 
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
1854 
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
1855 
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build/c_m_dc.html View File

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1295 
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1296 
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
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+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
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1644 
 <p class="author">Author: Jean-Sébastien Caux</p>
 1644 
 <p class="author">Author: Jean-Sébastien Caux</p>
1645 
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
1645 
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1646 
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build/c_m_dc_curl.html View File

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1294 
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1295 
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1296 
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
1296 
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
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1646 
 <p class="author">Author: Jean-Sébastien Caux</p>
 1646 
 <p class="author">Author: Jean-Sébastien Caux</p>
1647 
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
1647 
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1648 
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build/c_m_dc_d2.html View File

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7 
 <title>Pre-Quantum Electrodynamics</title>
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 <title>Pre-Quantum Electrodynamics</title>
1293 
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 </summary>
1294 
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 <ul>
1295 
 <li>
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 <li>
1296 
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
1296 
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
1297
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1616 
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1617
1617
1618 
-<div id="outline-container-org78664e4" class="outline-6">
1619 
-<h6 id="org78664e4"><a href="#org78664e4">Divergence of gradient</a></h6>
1620 
-<div class="outline-text-6" id="text-org78664e4">
1618 
+<div id="outline-container-org873f1bb" class="outline-6">
1619 
+<h6 id="org873f1bb"><a href="#org873f1bb">Divergence of gradient</a></h6>
1620 
+<div class="outline-text-6" id="text-org873f1bb">
1621 
 <p>
 1621 
 <p>
1622 
 \({\boldsymbol \nabla} \cdot ({\boldsymbol \nabla} T) \equiv {\boldsymbol \nabla}^2 T\) is called the <b>Laplacian</b> of the scalar field \(T\).
 1622 
 \({\boldsymbol \nabla} \cdot ({\boldsymbol \nabla} T) \equiv {\boldsymbol \nabla}^2 T\) is called the <b>Laplacian</b> of the scalar field \(T\).
1623 
 The Laplacian of a vector field \({\boldsymbol \nabla}^2 {\bf v}\) is also defined as the vector with components
 1623 
 The Laplacian of a vector field \({\boldsymbol \nabla}^2 {\bf v}\) is also defined as the vector with components
1626 
 </div>
 1626 
 </div>
1627 
 </div>
 1627 
 </div>
1628
1628
1629 
-<div id="outline-container-orgecb53d1" class="outline-6">
1630 
-<h6 id="orgecb53d1"><a href="#orgecb53d1">Curl of a gradient</a></h6>
1631 
-<div class="outline-text-6" id="text-orgecb53d1">
1629 
+<div id="outline-container-orged6374e" class="outline-6">
1630 
+<h6 id="orged6374e"><a href="#orged6374e">Curl of a gradient</a></h6>
1631 
+<div class="outline-text-6" id="text-orged6374e">
1632 
 <p>
 1632 
 <p>
1633 
 This always vanishes.
 1633 
 This always vanishes.
1634 
 </p>
 1634 
 </p>
1635 
 </div>
 1635 
 </div>
1636 
 </div>
 1636 
 </div>
1637
1637
1638 
-<div id="outline-container-orgdeab960" class="outline-6">
1639 
-<h6 id="orgdeab960"><a href="#orgdeab960">Gradient of the divergence</a></h6>
1640 
-<div class="outline-text-6" id="text-orgdeab960">
1638 
+<div id="outline-container-orgcf8bc6c" class="outline-6">
1639 
+<h6 id="orgcf8bc6c"><a href="#orgcf8bc6c">Gradient of the divergence</a></h6>
1640 
+<div class="outline-text-6" id="text-orgcf8bc6c">
1641 
 <p>
 1641 
 <p>
1642 
 \({\boldsymbol \nabla} ({\boldsymbol \nabla} \cdot {\bf v})\) does not appear often in physics.  No special name.
 1642 
 \({\boldsymbol \nabla} ({\boldsymbol \nabla} \cdot {\bf v})\) does not appear often in physics.  No special name.
1643 
 </p>
 1643 
 </p>
1644 
 </div>
 1644 
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1645 
 </div>
 1645 
 </div>
1646
1646
1647 
-<div id="outline-container-org11519c8" class="outline-6">
1648 
-<h6 id="org11519c8"><a href="#org11519c8">Divergence of a curl</a></h6>
1649 
-<div class="outline-text-6" id="text-org11519c8">
1647 
+<div id="outline-container-orgc1dc4c7" class="outline-6">
1648 
+<h6 id="orgc1dc4c7"><a href="#orgc1dc4c7">Divergence of a curl</a></h6>
1649 
+<div class="outline-text-6" id="text-orgc1dc4c7">
1650 
 <p>
 1650 
 <p>
1651 
 This always vanishes.
 1651 
 This always vanishes.
1652 
 </p>
 1652 
 </p>
1653 
 </div>
 1653 
 </div>
1654 
 </div>
 1654 
 </div>
1655
1655
1656 
-<div id="outline-container-org8bb99ae" class="outline-6">
1657 
-<h6 id="org8bb99ae"><a href="#org8bb99ae">Curl of curl</a></h6>
1658 
-<div class="outline-text-6" id="text-org8bb99ae">
1659 
-<div class="eqlabel" id="org38dd889">
1656 
+<div id="outline-container-org766740d" class="outline-6">
1657 
+<h6 id="org766740d"><a href="#org766740d">Curl of curl</a></h6>
1658 
+<div class="outline-text-6" id="text-org766740d">
1659 
+<div class="eqlabel" id="orga94a832">
1660 
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 1660 
 <p>
1661 
 <a id="curlcurl"></a><a href="./c_m_dc_d2.html#curlcurl"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
 1661 
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1662 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
 1662 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
1663 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 1663 
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1664 
 </svg></a>
 1664 
 </svg></a>
1665 
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 1665 
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1666 
-<div class="alteqlabels" id="orgb8e88ad">
1666 
+<div class="alteqlabels" id="orgc3745e4">
1667
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1668 
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1669
1669
1694 
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1695 
 <div id="postamble" class="status">
 1695 
 <div id="postamble" class="status">
1696 
 <p class="author">Author: Jean-Sébastien Caux</p>
 1696 
 <p class="author">Author: Jean-Sébastien Caux</p>
1697 
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
1697 
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
1698 
 <p class="validation"></p>
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build/c_m_dc_del.html View File

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 <title>Pre-Quantum Electrodynamics</title>
1293 
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 </summary>
1294 
 <ul>
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 <ul>
1295 
 <li>
 1295 
 <li>
1296 
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
1296 
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
1297
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1645 
 <p class="author">Author: Jean-Sébastien Caux</p>
 1645 
 <p class="author">Author: Jean-Sébastien Caux</p>
1646 
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
1646 
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
1647 
 <p class="validation"></p>
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build/c_m_dc_div.html View File

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7 
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 7 
 <title>Pre-Quantum Electrodynamics</title>
1293 
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 1293 
 </summary>
1294 
 <ul>
 1294 
 <ul>
1295 
 <li>
 1295 
 <li>
1296 
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
1296 
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
1297
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1298 
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1299
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1640 
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 1640 
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1641 
 <div id="postamble" class="status">
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 <div id="postamble" class="status">
1642 
 <p class="author">Author: Jean-Sébastien Caux</p>
 1642 
 <p class="author">Author: Jean-Sébastien Caux</p>
1643 
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
1643 
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
1644 
 <p class="validation"></p>
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build/c_m_dc_g.html View File

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7 
 <title>Pre-Quantum Electrodynamics</title>
 7 
 <title>Pre-Quantum Electrodynamics</title>
1293 
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 1293 
 </summary>
1294 
 <ul>
 1294 
 <ul>
1295 
 <li>
 1295 
 <li>
1296 
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
1296 
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
1297
1297
1298 
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 1298 
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1299
1299
1664 
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 1664 
 </div>
1665 
 <div id="postamble" class="status">
 1665 
 <div id="postamble" class="status">
1666 
 <p class="author">Author: Jean-Sébastien Caux</p>
 1666 
 <p class="author">Author: Jean-Sébastien Caux</p>
1667 
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
1667 
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
1668 
 <p class="validation"></p>
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build/c_m_dc_pr.html View File

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+<!-- 2022-03-24 Thu 08:42 -->
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 <meta name="viewport" content="width=device-width, initial-scale=1">
7 
 <title>Pre-Quantum Electrodynamics</title>
 7 
 <title>Pre-Quantum Electrodynamics</title>
1293 
 </summary>
 1293 
 </summary>
1294 
 <ul>
 1294 
 <ul>
1295 
 <li>
 1295 
 <li>
1296 
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
1296 
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
1297
1297
1298 
 </li>
 1298 
 </li>
1299
1299
1622 
 <p>
 1622 
 <p>
1623 
 <b>Gradient of a product</b>:
 1623 
 <b>Gradient of a product</b>:
1624 
 </p>
 1624 
 </p>
1625 
-<div class="eqlabel" id="org89b1475">
1625 
+<div class="eqlabel" id="orge6e6a80">
1626 
 <p>
 1626 
 <p>
1627 
 <a id="grad_prod"></a><a href="./c_m_dc_pr.html#grad_prod"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
 1627 
 <a id="grad_prod"></a><a href="./c_m_dc_pr.html#grad_prod"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
1628 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
 1628 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
1629 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 1629 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
1630 
 </svg></a>
 1630 
 </svg></a>
1631 
 </p>
 1631 
 </p>
1632 
-<div class="alteqlabels" id="orgc71740f">
1632 
+<div class="alteqlabels" id="orgf9842ae">
1633 
 <ul class="org-ul">
 1633 
 <ul class="org-ul">
1634 
 <li>Gr (3)</li>
 1634 
 <li>Gr (3)</li>
1635 
 <li>W (1-111)</li>
 1635 
 <li>W (1-111)</li>
1649 
 <p>
 1649 
 <p>
1650 
 <b>Gradient of a scalar product</b>:
 1650 
 <b>Gradient of a scalar product</b>:
1651 
 </p>
 1651 
 </p>
1652 
-<div class="eqlabel" id="orgdcd103a">
1652 
+<div class="eqlabel" id="orgb8556f5">
1653 
 <p>
 1653 
 <p>
1654 
 <a id="grad_sprod"></a><a href="./c_m_dc_pr.html#grad_sprod"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
 1654 
 <a id="grad_sprod"></a><a href="./c_m_dc_pr.html#grad_sprod"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
1655 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
 1655 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
1656 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 1656 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
1657 
 </svg></a>
 1657 
 </svg></a>
1658 
 </p>
 1658 
 </p>
1659 
-<div class="alteqlabels" id="org5dbb766">
1659 
+<div class="alteqlabels" id="org884e962">
1660 
 <ul class="org-ul">
 1660 
 <ul class="org-ul">
1661 
 <li>Gr (4)</li>
 1661 
 <li>Gr (4)</li>
1662 
 <li>W (1-112)</li>
 1662 
 <li>W (1-112)</li>
1676 
 <p>
 1676 
 <p>
1677 
 <b>Divergence of a product</b>:
 1677 
 <b>Divergence of a product</b>:
1678 
 </p>
 1678 
 </p>
1679 
-<div class="eqlabel" id="org16aa48b">
1679 
+<div class="eqlabel" id="org3da56b1">
1680 
 <p>
 1680 
 <p>
1681 
 <a id="div_prod"></a><a href="./c_m_dc_pr.html#div_prod"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
 1681 
 <a id="div_prod"></a><a href="./c_m_dc_pr.html#div_prod"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
1682 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
 1682 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
1683 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 1683 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
1684 
 </svg></a>
 1684 
 </svg></a>
1685 
 </p>
 1685 
 </p>
1686 
-<div class="alteqlabels" id="org03b99ec">
1686 
+<div class="alteqlabels" id="orgeb30387">
1687 
 <ul class="org-ul">
 1687 
 <ul class="org-ul">
1688 
 <li>Gr (5)</li>
 1688 
 <li>Gr (5)</li>
1689 
 <li>W (1-115)</li>
 1689 
 <li>W (1-115)</li>
1703 
 <p>
 1703 
 <p>
1704 
 <b>Divergence of a cross product</b>:
 1704 
 <b>Divergence of a cross product</b>:
1705 
 </p>
 1705 
 </p>
1706 
-<div class="eqlabel" id="orga48567e">
1706 
+<div class="eqlabel" id="orgbfaa39d">
1707 
 <p>
 1707 
 <p>
1708 
 <a id="div_xprod"></a><a href="./c_m_dc_pr.html#div_xprod"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
 1708 
 <a id="div_xprod"></a><a href="./c_m_dc_pr.html#div_xprod"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
1709 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
 1709 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
1710 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 1710 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
1711 
 </svg></a>
 1711 
 </svg></a>
1712 
 </p>
 1712 
 </p>
1713 
-<div class="alteqlabels" id="org0aece97">
1713 
+<div class="alteqlabels" id="orgca8e0c0">
1714 
 <ul class="org-ul">
 1714 
 <ul class="org-ul">
1715 
 <li>Gr (6)</li>
 1715 
 <li>Gr (6)</li>
1716 
 <li>W (1-116)</li>
 1716 
 <li>W (1-116)</li>
1730 
 <p>
 1730 
 <p>
1731 
 <b>Curl of a product</b>:
 1731 
 <b>Curl of a product</b>:
1732 
 </p>
 1732 
 </p>
1733 
-<div class="eqlabel" id="org3dec348">
1733 
+<div class="eqlabel" id="org5b32772">
1734 
 <p>
 1734 
 <p>
1735 
 <a id="curl_prod"></a><a href="./c_m_dc_pr.html#curl_prod"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
 1735 
 <a id="curl_prod"></a><a href="./c_m_dc_pr.html#curl_prod"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
1736 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
 1736 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
1737 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 1737 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
1738 
 </svg></a>
 1738 
 </svg></a>
1739 
 </p>
 1739 
 </p>
1740 
-<div class="alteqlabels" id="orgd0f6f07">
1740 
+<div class="alteqlabels" id="org22a6f09">
1741 
 <ul class="org-ul">
 1741 
 <ul class="org-ul">
1742 
 <li>Gr (7)</li>
 1742 
 <li>Gr (7)</li>
1743 
 <li>W (1-118)</li>
 1743 
 <li>W (1-118)</li>
1757 
 <p>
 1757 
 <p>
1758 
 <b>Curl of a cross product</b>:
 1758 
 <b>Curl of a cross product</b>:
1759 
 </p>
 1759 
 </p>
1760 
-<div class="eqlabel" id="orga9f7b57">
1760 
+<div class="eqlabel" id="org81448bf">
1761 
 <p>
 1761 
 <p>
1762 
 <a id="curl_xprod"></a><a href="./c_m_dc_pr.html#curl_xprod"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
 1762 
 <a id="curl_xprod"></a><a href="./c_m_dc_pr.html#curl_xprod"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
1763 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
 1763 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
1764 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 1764 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
1765 
 </svg></a>
 1765 
 </svg></a>
1766 
 </p>
 1766 
 </p>
1767 
-<div class="alteqlabels" id="org69dc8a6">
1767 
+<div class="alteqlabels" id="org5de3f60">
1768 
 <ul class="org-ul">
 1768 
 <ul class="org-ul">
1769 
 <li>Gr (8)</li>
 1769 
 <li>Gr (8)</li>
1770 
 <li>W (1-119)</li>
 1770 
 <li>W (1-119)</li>
1805 
 </div>
 1805 
 </div>
1806 
 <div id="postamble" class="status">
 1806 
 <div id="postamble" class="status">
1807 
 <p class="author">Author: Jean-Sébastien Caux</p>
 1807 
 <p class="author">Author: Jean-Sébastien Caux</p>
1808 
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
1808 
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
1809 
 <p class="validation"></p>
 1809 
 <p class="validation"></p>
1810 
 </div>
 1810 
 </div>
1811
1811

+ 3
- 3
build/c_m_dd.html View File

1 
 <!DOCTYPE html>
 1 
 <!DOCTYPE html>
2 
 <html lang="en">
 2 
 <html lang="en">
3 
 <head>
 3 
 <head>
4 
-<!-- 2022-03-22 Tue 10:52 -->
4 
+<!-- 2022-03-24 Thu 08:42 -->
5 
 <meta charset="utf-8">
 5 
 <meta charset="utf-8">
6 
 <meta name="viewport" content="width=device-width, initial-scale=1">
 6 
 <meta name="viewport" content="width=device-width, initial-scale=1">
7 
 <title>Pre-Quantum Electrodynamics</title>
 7 
 <title>Pre-Quantum Electrodynamics</title>
1293 
 </summary>
 1293 
 </summary>
1294 
 <ul>
 1294 
 <ul>
1295 
 <li>
 1295 
 <li>
1296 
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
1296 
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
1297
1297
1298 
 </li>
 1298 
 </li>
1299
1299
1639 
 </div>
 1639 
 </div>
1640 
 <div id="postamble" class="status">
 1640 
 <div id="postamble" class="status">
1641 
 <p class="author">Author: Jean-Sébastien Caux</p>
 1641 
 <p class="author">Author: Jean-Sébastien Caux</p>
1642 
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
1642 
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
1643 
 <p class="validation"></p>
 1643 
 <p class="validation"></p>
1644 
 </div>
 1644 
 </div>
1645
1645

+ 3
- 3
build/c_m_dd_1d.html View File

1 
 <!DOCTYPE html>
 1 
 <!DOCTYPE html>
2 
 <html lang="en">
 2 
 <html lang="en">
3 
 <head>
 3 
 <head>
4 
-<!-- 2022-03-22 Tue 10:52 -->
4 
+<!-- 2022-03-24 Thu 08:42 -->
5 
 <meta charset="utf-8">
 5 
 <meta charset="utf-8">
6 
 <meta name="viewport" content="width=device-width, initial-scale=1">
 6 
 <meta name="viewport" content="width=device-width, initial-scale=1">
7 
 <title>Pre-Quantum Electrodynamics</title>
 7 
 <title>Pre-Quantum Electrodynamics</title>
1293 
 </summary>
 1293 
 </summary>
1294 
 <ul>
 1294 
 <ul>
1295 
 <li>
 1295 
 <li>
1296 
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
1296 
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
1297
1297
1298 
 </li>
 1298 
 </li>
1299
1299
1651 
 </div>
 1651 
 </div>
1652 
 <div id="postamble" class="status">
 1652 
 <div id="postamble" class="status">
1653 
 <p class="author">Author: Jean-Sébastien Caux</p>
 1653 
 <p class="author">Author: Jean-Sébastien Caux</p>
1654 
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
1654 
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
1655 
 <p class="validation"></p>
 1655 
 <p class="validation"></p>
1656 
 </div>
 1656 
 </div>
1657
1657

+ 9
- 9
build/c_m_dd_3d.html View File

1 
 <!DOCTYPE html>
 1 
 <!DOCTYPE html>
2 
 <html lang="en">
 2 
 <html lang="en">
3 
 <head>
 3 
 <head>
4 
-<!-- 2022-03-22 Tue 10:52 -->
4 
+<!-- 2022-03-24 Thu 08:42 -->
5 
 <meta charset="utf-8">
 5 
 <meta charset="utf-8">
6 
 <meta name="viewport" content="width=device-width, initial-scale=1">
 6 
 <meta name="viewport" content="width=device-width, initial-scale=1">
7 
 <title>Pre-Quantum Electrodynamics</title>
 7 
 <title>Pre-Quantum Electrodynamics</title>
1293 
 </summary>
 1293 
 </summary>
1294 
 <ul>
 1294 
 <ul>
1295 
 <li>
 1295 
 <li>
1296 
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
1296 
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
1297
1297
1298 
 </li>
 1298 
 </li>
1299
1299
1636 
 More generally,
 1636 
 More generally,
1637 
 </p>
 1637 
 </p>
1638
1638
1639 
-<div class="eqlabel" id="orga7ea793">
1639 
+<div class="eqlabel" id="orgcf3b8a6">
1640 
 <p>
 1640 
 <p>
1641 
 <a id="divdel"></a><a href="./c_m_dd_3d.html#divdel"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
 1641 
 <a id="divdel"></a><a href="./c_m_dd_3d.html#divdel"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
1642 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
 1642 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
1643 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 1643 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
1644 
 </svg></a>
 1644 
 </svg></a>
1645 
 </p>
 1645 
 </p>
1646 
-<div class="alteqlabels" id="org2afb48e">
1646 
+<div class="alteqlabels" id="orgd295657">
1647 
 <ul class="org-ul">
 1647 
 <ul class="org-ul">
1648 
 <li>Gr (1.100)</li>
 1648 
 <li>Gr (1.100)</li>
1649 
 </ul>
 1649 
 </ul>
1662 
 Since
 1662 
 Since
1663 
 </p>
 1663 
 </p>
1664
1664
1665 
-<div class="eqlabel" id="org0791e6b">
1665 
+<div class="eqlabel" id="org8e3f2ff">
1666 
 <p>
 1666 
 <p>
1667 
 <a id="div1or"></a><a href="./c_m_dd_3d.html#div1or"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
 1667 
 <a id="div1or"></a><a href="./c_m_dd_3d.html#div1or"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
1668 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
 1668 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
1669 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 1669 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
1670 
 </svg></a>
 1670 
 </svg></a>
1671 
 </p>
 1671 
 </p>
1672 
-<div class="alteqlabels" id="org5b1c286">
1672 
+<div class="alteqlabels" id="orgd9d8d13">
1673 
 <ul class="org-ul">
 1673 
 <ul class="org-ul">
1674 
 <li>Gr (1.101)</li>
 1674 
 <li>Gr (1.101)</li>
1675 
 </ul>
 1675 
 </ul>
1685 
 <p>
 1685 
 <p>
1686 
 we have that
 1686 
 we have that
1687 
 </p>
 1687 
 </p>
1688 
-<div class="eqlabel" id="org72632aa">
1688 
+<div class="eqlabel" id="org4584082">
1689 
 <p>
 1689 
 <p>
1690 
 <a id="Lap1or"></a><a href="./c_m_dd_3d.html#Lap1or"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
 1690 
 <a id="Lap1or"></a><a href="./c_m_dd_3d.html#Lap1or"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
1691 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
 1691 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
1692 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 1692 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
1693 
 </svg></a>
 1693 
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 \[
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 {\int_{\bf a}^{\bf b}}_{\cal P} {\bf v} \cdot d{\bf l}
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 {\int_{\bf a}^{\bf b}}_{\cal P} {\bf v} \cdot d{\bf l}
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 \int_{\cal S} {\bf v} \cdot d{\bf a}
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1655 
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1643 
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
1644 
 <p class="validation"></p>
 1644 
 <p class="validation"></p>
1645 
 </div>
 1645 
 </div>
1646
1646

+ 14
- 14
build/emd_Fl_Fl.html View File

1 
 <!DOCTYPE html>
 1 
 <!DOCTYPE html>
2 
 <html lang="en">
 2 
 <html lang="en">
3 
 <head>
 3 
 <head>
4 
-<!-- 2022-03-22 Tue 10:52 -->
4 
+<!-- 2022-03-24 Thu 08:42 -->
5 
 <meta charset="utf-8">
 5 
 <meta charset="utf-8">
6 
 <meta name="viewport" content="width=device-width, initial-scale=1">
 6 
 <meta name="viewport" content="width=device-width, initial-scale=1">
7 
 <title>Pre-Quantum Electrodynamics</title>
 7 
 <title>Pre-Quantum Electrodynamics</title>
1293 
 </summary>
 1293 
 </summary>
1294 
 <ul>
 1294 
 <ul>
1295 
 <li>
 1295 
 <li>
1296 
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
1296 
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
1297
1297
1298 
 </li>
 1298 
 </li>
1299
1299
1644 
 the circuit. This current is really driven by an electric field having a component
 1644 
 the circuit. This current is really driven by an electric field having a component
1645 
 along the wire.  The line integral of this field is called the
 1645 
 along the wire.  The line integral of this field is called the
1646 
 </p>
 1646 
 </p>
1647 
-<div class="core div" id="orgc1ab4b8">
1647 
+<div class="core div" id="orgb0fd5b4">
1648 
 <p>
 1648 
 <p>
1649 
 <b>Electromotive force (or electromotance)</b>,
 1649 
 <b>Electromotive force (or electromotance)</b>,
1650 
 </p>
 1650 
 </p>
1651 
-<div class="eqlabel" id="org1ce0462">
1651 
+<div class="eqlabel" id="orgb0e7cde">
1652 
 <p>
 1652 
 <p>
1653 
 <a id="elmofo"></a><a href="./emd_Fl_Fl.html#elmofo"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
 1653 
 <a id="elmofo"></a><a href="./emd_Fl_Fl.html#elmofo"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
1654 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
 1654 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
1655 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 1655 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
1656 
 </svg></a>
 1656 
 </svg></a>
1657 
 </p>
 1657 
 </p>
1658 
-<div class="alteqlabels" id="orge2b1b8b">
1658 
+<div class="alteqlabels" id="org516a196">
1659 
 <ul class="org-ul">
 1659 
 <ul class="org-ul">
1660 
 <li>Gr (7.9)</li>
 1660 
 <li>Gr (7.9)</li>
1661 
 </ul>
 1661 
 </ul>
1680 
 is that the electromotive force is proportional
 1680 
 is that the electromotive force is proportional
1681 
 to the rate of change of the magnetic flux,
 1681 
 to the rate of change of the magnetic flux,
1682 
 </p>
 1682 
 </p>
1683 
-<div class="eqlabel" id="orgb4b21bf">
1683 
+<div class="eqlabel" id="orgab619b1">
1684 
 <p>
 1684 
 <p>
1685 
 <a id="Fl_flux"></a><a href="./emd_Fl_Fl.html#Fl_flux"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
 1685 
 <a id="Fl_flux"></a><a href="./emd_Fl_Fl.html#Fl_flux"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
1686 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
 1686 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
1687 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 1687 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
1688 
 </svg></a>
 1688 
 </svg></a>
1689 
 </p>
 1689 
 </p>
1690 
-<div class="alteqlabels" id="org4e36847">
1690 
+<div class="alteqlabels" id="org969857c">
1691 
 <ul class="org-ul">
 1691 
 <ul class="org-ul">
1692 
 <li>Gr (7.14)</li>
 1692 
 <li>Gr (7.14)</li>
1693 
 </ul>
 1693 
 </ul>
1702 
 \]
 1702 
 \]
1703 
 so we obtain
 1703 
 so we obtain
1704 
 </p>
 1704 
 </p>
1705 
-<div class="core div" id="org3b354eb">
1705 
+<div class="core div" id="org5419feb">
1706 
 <p>
 1706 
 <p>
1707 
 <b>Faraday's law</b> (integral form <i>N.B.: for a stationary loop</i>)
 1707 
 <b>Faraday's law</b> (integral form <i>N.B.: for a stationary loop</i>)
1708 
 </p>
 1708 
 </p>
1709 
-<div class="eqlabel" id="org3323690">
1709 
+<div class="eqlabel" id="org4696e9f">
1710 
 <p>
 1710 
 <p>
1711 
 <a id="Fl_int"></a><a href="./emd_Fl_Fl.html#Fl_int"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
 1711 
 <a id="Fl_int"></a><a href="./emd_Fl_Fl.html#Fl_int"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
1712 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
 1712 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
1713 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 1713 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
1714 
 </svg></a>
 1714 
 </svg></a>
1715 
 </p>
 1715 
 </p>
1716 
-<div class="alteqlabels" id="orgc991325">
1716 
+<div class="alteqlabels" id="org439dfef">
1717 
 <ul class="org-ul">
 1717 
 <ul class="org-ul">
1718 
 <li>Gr (7.15)</li>
 1718 
 <li>Gr (7.15)</li>
1719 
 </ul>
 1719 
 </ul>
1737 
 \]
 1737 
 \]
1738 
 we obtain
 1738 
 we obtain
1739 
 </p>
 1739 
 </p>
1740 
-<div class="core div" id="org5eb686c">
1741 
-<div class="eqlabel" id="org7ca80cd">
1740 
+<div class="core div" id="org49ffd42">
1741 
+<div class="eqlabel" id="org5ecebad">
1742 
 <p>
 1742 
 <p>
1743 
 <a id="Fl"></a><a href="./emd_Fl_Fl.html#Fl"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
 1743 
 <a id="Fl"></a><a href="./emd_Fl_Fl.html#Fl"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
1744 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
 1744 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
1745 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 1745 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
1746 
 </svg></a>
 1746 
 </svg></a>
1747 
 </p>
 1747 
 </p>
1748 
-<div class="alteqlabels" id="org859ac4a">
1748 
+<div class="alteqlabels" id="org6a61522">
1749 
 <ul class="org-ul">
 1749 
 <ul class="org-ul">
1750 
 <li>Gr (7.16)</li>
 1750 
 <li>Gr (7.16)</li>
1751 
 </ul>
 1751 
 </ul>
1790 
 </div>
 1790 
 </div>
1791 
 <div id="postamble" class="status">
 1791 
 <div id="postamble" class="status">
1792 
 <p class="author">Author: Jean-Sébastien Caux</p>
 1792 
 <p class="author">Author: Jean-Sébastien Caux</p>
1793 
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
1793 
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
1794 
 <p class="validation"></p>
 1794 
 <p class="validation"></p>
1795 
 </div>
 1795 
 </div>
1796
1796

+ 9
- 9
build/emd_Fl_e.html View File

1 
 <!DOCTYPE html>
 1 
 <!DOCTYPE html>
2 
 <html lang="en">
 2 
 <html lang="en">
3 
 <head>
 3 
 <head>
4 
-<!-- 2022-03-22 Tue 10:52 -->
4 
+<!-- 2022-03-24 Thu 08:42 -->
5 
 <meta charset="utf-8">
 5 
 <meta charset="utf-8">
6 
 <meta name="viewport" content="width=device-width, initial-scale=1">
 6 
 <meta name="viewport" content="width=device-width, initial-scale=1">
7 
 <title>Pre-Quantum Electrodynamics</title>
 7 
 <title>Pre-Quantum Electrodynamics</title>
1293 
 </summary>
 1293 
 </summary>
1294 
 <ul>
 1294 
 <ul>
1295 
 <li>
 1295 
 <li>
1296 
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
1296 
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
1297
1297
1298 
 </li>
 1298 
 </li>
1299
1299
1639 
 \]
 1639 
 \]
1640 
 Generalization to volume currents:
 1640 
 Generalization to volume currents:
1641 
 </p>
 1641 
 </p>
1642 
-<div class="eqlabel" id="org3409c0a">
1642 
+<div class="eqlabel" id="orge9580af">
1643 
 <p>
 1643 
 <p>
1644 
 <a id="W_intAJ"></a><a href="./emd_Fl_e.html#W_intAJ"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
 1644 
 <a id="W_intAJ"></a><a href="./emd_Fl_e.html#W_intAJ"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
1645 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
 1645 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
1646 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 1646 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
1647 
 </svg></a>
 1647 
 </svg></a>
1648 
 </p>
 1648 
 </p>
1649 
-<div class="alteqlabels" id="org84f1d51">
1649 
+<div class="alteqlabels" id="orgbe0c60a">
1650 
 <ul class="org-ul">
 1650 
 <ul class="org-ul">
1651 
 <li>Gr (7.31)</li>
 1651 
 <li>Gr (7.31)</li>
1652 
 </ul>
 1652 
 </ul>
1681 
 \]
 1681 
 \]
1682 
 We can integrate over all space:  after neglecting boundary terms (assuming fields fall to zero at infinity), we are left with
 1682 
 We can integrate over all space:  after neglecting boundary terms (assuming fields fall to zero at infinity), we are left with
1683 
 </p>
 1683 
 </p>
1684 
-<div class="core div" id="orgced7757">
1685 
-<div class="eqlabel" id="orgd899514">
1684 
+<div class="core div" id="org9173f2d">
1685 
+<div class="eqlabel" id="org717e156">
1686 
 <p>
 1686 
 <p>
1687 
 <a id="W_intBsq"></a><a href="./emd_Fl_e.html#W_intBsq"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
 1687 
 <a id="W_intBsq"></a><a href="./emd_Fl_e.html#W_intBsq"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
1688 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
 1688 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
1689 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 1689 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
1690 
 </svg></a>
 1690 
 </svg></a>
1691 
 </p>
 1691 
 </p>
1692 
-<div class="alteqlabels" id="orgf7c92a2">
1692 
+<div class="alteqlabels" id="org0d5a0b3">
1693 
 <ul class="org-ul">
 1693 
 <ul class="org-ul">
1694 
 <li>Gr (7.34)</li>
 1694 
 <li>Gr (7.34)</li>
1695 
 </ul>
 1695 
 </ul>
1718 
 which are equations <a href="./ems_es_e.html#W_vcd">W_vcd</a>, <a href="./ems_es_e.html#W_intEsq">W_intEsq</a>, <a href="./emd_Fl_e.html#W_intAJ">W_intAJ</a> and <a href="./emd_Fl_e.html#W_intBsq">W_intBsq</a>.
 1718 
 which are equations <a href="./ems_es_e.html#W_vcd">W_vcd</a>, <a href="./ems_es_e.html#W_intEsq">W_intEsq</a>, <a href="./emd_Fl_e.html#W_intAJ">W_intAJ</a> and <a href="./emd_Fl_e.html#W_intBsq">W_intBsq</a>.
1719 
 </p>
 1719 
 </p>
1720
1720
1721 
-<div class="example div" id="orge558476">
1721 
+<div class="example div" id="org34d5a7d">
1722 
 <p>
 1722 
 <p>
1723 
 <b>Example: energy in coaxial cable</b>
 1723 
 <b>Example: energy in coaxial cable</b>
1724 
 </p>
 1724 
 </p>
1768 
 </div>
 1768 
 </div>
1769 
 <div id="postamble" class="status">
 1769 
 <div id="postamble" class="status">
1770 
 <p class="author">Author: Jean-Sébastien Caux</p>
 1770 
 <p class="author">Author: Jean-Sébastien Caux</p>
1771 
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
1771 
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
1772 
 <p class="validation"></p>
 1772 
 <p class="validation"></p>
1773 
 </div>
 1773 
 </div>
1774
1774

+ 12
- 12
build/emd_Fl_i.html View File

1 
 <!DOCTYPE html>
 1 
 <!DOCTYPE html>
2 
 <html lang="en">
 2 
 <html lang="en">
3 
 <head>
 3 
 <head>
4 
-<!-- 2022-03-22 Tue 10:52 -->
4 
+<!-- 2022-03-24 Thu 08:42 -->
5 
 <meta charset="utf-8">
 5 
 <meta charset="utf-8">
6 
 <meta name="viewport" content="width=device-width, initial-scale=1">
 6 
 <meta name="viewport" content="width=device-width, initial-scale=1">
7 
 <title>Pre-Quantum Electrodynamics</title>
 7 
 <title>Pre-Quantum Electrodynamics</title>
1293 
 </summary>
 1293 
 </summary>
1294 
 <ul>
 1294 
 <ul>
1295 
 <li>
 1295 
 <li>
1296 
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
1296 
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
1297
1297
1298 
 </li>
 1298 
 </li>
1299
1299
1641 
 \]
 1641 
 \]
1642 
 and we can write the mutual inductance as the <b>Neumann formula</b>,
 1642 
 and we can write the mutual inductance as the <b>Neumann formula</b>,
1643 
 </p>
 1643 
 </p>
1644 
-<div class="eqlabel" id="org3ec4c18">
1644 
+<div class="eqlabel" id="org1f70ff2">
1645 
 <p>
 1645 
 <p>
1646 
 <a id="Newmann_M"></a><a href="./emd_Fl_i.html#Newmann_M"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
 1646 
 <a id="Newmann_M"></a><a href="./emd_Fl_i.html#Newmann_M"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
1647 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
 1647 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
1648 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 1648 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
1649 
 </svg></a>
 1649 
 </svg></a>
1650 
 </p>
 1650 
 </p>
1651 
-<div class="alteqlabels" id="org7ff8d1e">
1651 
+<div class="alteqlabels" id="org57de753">
1652 
 <ul class="org-ul">
 1652 
 <ul class="org-ul">
1653 
 <li>Gr (7.22)</li>
 1653 
 <li>Gr (7.22)</li>
1654 
 </ul>
 1654 
 </ul>
1665 
 Two things:
 1665 
 Two things:
1666 
 first, \(M_{21}\) is purely geometrical.  Second,
 1666 
 first, \(M_{21}\) is purely geometrical.  Second,
1667 
 </p>
 1667 
 </p>
1668 
-<div class="eqlabel" id="orge7f5edd">
1668 
+<div class="eqlabel" id="org43668cc">
1669 
 <p>
 1669 
 <p>
1670 
 <a id="Msym"></a><a href="./emd_Fl_i.html#Msym"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
 1670 
 <a id="Msym"></a><a href="./emd_Fl_i.html#Msym"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
1671 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
 1671 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
1672 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 1672 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
1673 
 </svg></a>
 1673 
 </svg></a>
1674 
 </p>
 1674 
 </p>
1675 
-<div class="alteqlabels" id="org54ddc77">
1675 
+<div class="alteqlabels" id="org7b1e4fa">
1676 
 <ul class="org-ul">
 1676 
 <ul class="org-ul">
1677 
 <li>Gr (7.23)</li>
 1677 
 <li>Gr (7.23)</li>
1678 
 </ul>
 1678 
 </ul>
1687 
 \]
 1687 
 \]
1688 
 </p>
 1688 
 </p>
1689
1689
1690 
-<div class="example div" id="org1bcebe3">
1690 
+<div class="example div" id="orgecf7176">
1691 
 <p>
 1691 
 <p>
1692 
 <b>Example: solenoid in solenoid</b>
 1692 
 <b>Example: solenoid in solenoid</b>
1693 
 </p>
 1693 
 </p>
1735 
 \]
 1735 
 \]
1736 
 Changing current also induces EMF in the source loop itself:
 1736 
 Changing current also induces EMF in the source loop itself:
1737 
 </p>
 1737 
 </p>
1738 
-<div class="eqlabel" id="orgdaaac4e">
1738 
+<div class="eqlabel" id="org2512f69">
1739 
 <p>
 1739 
 <p>
1740 
 <a id="PLI"></a><a href="./emd_Fl_i.html#PLI"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
 1740 
 <a id="PLI"></a><a href="./emd_Fl_i.html#PLI"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
1741 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
 1741 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
1742 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 1742 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
1743 
 </svg></a>
 1743 
 </svg></a>
1744 
 </p>
 1744 
 </p>
1745 
-<div class="alteqlabels" id="orgb8faf94">
1745 
+<div class="alteqlabels" id="org080d683">
1746 
 <ul class="org-ul">
 1746 
 <ul class="org-ul">
1747 
 <li>Gr (7.25)</li>
 1747 
 <li>Gr (7.25)</li>
1748 
 </ul>
 1748 
 </ul>
1765 
 </p>
 1765 
 </p>
1766
1766
1767
1767
1768 
-<div class="example div" id="org11544ba">
1768 
+<div class="example div" id="orgce99b7c">
1769 
 <p>
 1769 
 <p>
1770 
 <b>Example: self-inductance of toroidal coil</b>
 1770 
 <b>Example: self-inductance of toroidal coil</b>
1771 
 </p>
 1771 
 </p>
1804 
 Think of <i>back EMF</i>.
 1804 
 Think of <i>back EMF</i>.
1805 
 </p>
 1805 
 </p>
1806
1806
1807 
-<div class="example div" id="org52373ca">
1807 
+<div class="example div" id="orgb4d543b">
1808 
 <p>
 1808 
 <p>
1809 
 <b>Example: circuit</b>
 1809 
 <b>Example: circuit</b>
1810 
 </p>
 1810 
 </p>
1853 
 </div>
 1853 
 </div>
1854 
 <div id="postamble" class="status">
 1854 
 <div id="postamble" class="status">
1855 
 <p class="author">Author: Jean-Sébastien Caux</p>
 1855 
 <p class="author">Author: Jean-Sébastien Caux</p>
1856 
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
1856 
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
1857 
 <p class="validation"></p>
 1857 
 <p class="validation"></p>
1858 
 </div>
 1858 
 </div>
1859
1859

+ 6
- 6
build/emd_Fl_ief.html View File

1 
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2 
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3 
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 <head>
4 
-<!-- 2022-03-22 Tue 10:52 -->
4 
+<!-- 2022-03-24 Thu 08:42 -->
5 
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 <meta charset="utf-8">
6 
 <meta name="viewport" content="width=device-width, initial-scale=1">
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 <meta name="viewport" content="width=device-width, initial-scale=1">
7 
 <title>Pre-Quantum Electrodynamics</title>
 7 
 <title>Pre-Quantum Electrodynamics</title>
1293 
 </summary>
 1293 
 </summary>
1294 
 <ul>
 1294 
 <ul>
1295 
 <li>
 1295 
 <li>
1296 
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
1296 
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
1297
1297
1298 
 </li>
 1298 
 </li>
1299
1299
1637
1637
1638
1638
1639
1639
1640 
-<div class="example div" id="orgfcd2e61">
1640 
+<div class="example div" id="org2badd21">
1641 
 <p>
 1641 
 <p>
1642 
 <b>Example: loop with time-dependent flux</b>
 1642 
 <b>Example: loop with time-dependent flux</b>
1643 
 </p>
 1643 
 </p>
1664 
 </div>
 1664 
 </div>
1665
1665
1666
1666
1667 
-<div class="example div" id="orgafdd47c">
1667 
+<div class="example div" id="org6994570">
1668 
 <p>
 1668 
 <p>
1669 
 <b>Example: wheel with charged rim traversed by flux</b>
 1669 
 <b>Example: wheel with charged rim traversed by flux</b>
1670 
 </p>
 1670 
 </p>
1705 
 <i>slow enough</i> phenomena.
 1705 
 <i>slow enough</i> phenomena.
1706 
 </p>
 1706 
 </p>
1707
1707
1708 
-<div class="example div" id="org6631fcc">
1708 
+<div class="example div" id="orgddce4f1">
1709 
 <p>
 1709 
 <p>
1710 
 <b>Example: field from wire with time-dependent current</b>
 1710 
 <b>Example: field from wire with time-dependent current</b>
1711 
 </p>
 1711 
 </p>
1764 
 </div>
 1764 
 </div>
1765 
 <div id="postamble" class="status">
 1765 
 <div id="postamble" class="status">
1766 
 <p class="author">Author: Jean-Sébastien Caux</p>
 1766 
 <p class="author">Author: Jean-Sébastien Caux</p>
1767 
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
1767 
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
1768 
 <p class="validation"></p>
 1768 
 <p class="validation"></p>
1769 
 </div>
 1769 
 </div>
1770
1770

+ 3
- 3
build/emd_Me.html View File

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2 
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3 
 <head>
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 <head>
4 
-<!-- 2022-03-22 Tue 10:52 -->
4 
+<!-- 2022-03-24 Thu 08:42 -->
5 
 <meta charset="utf-8">
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 <meta charset="utf-8">
6 
 <meta name="viewport" content="width=device-width, initial-scale=1">
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 <meta name="viewport" content="width=device-width, initial-scale=1">
7 
 <title>Pre-Quantum Electrodynamics</title>
 7 
 <title>Pre-Quantum Electrodynamics</title>
1293 
 </summary>
 1293 
 </summary>
1294 
 <ul>
 1294 
 <ul>
1295 
 <li>
 1295 
 <li>
1296 
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
1296 
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
1297
1297
1298 
 </li>
 1298 
 </li>
1299
1299
1640 
 </div>
 1640 
 </div>
1641 
 <div id="postamble" class="status">
 1641 
 <div id="postamble" class="status">
1642 
 <p class="author">Author: Jean-Sébastien Caux</p>
 1642 
 <p class="author">Author: Jean-Sébastien Caux</p>
1643 
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
1643 
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
1644 
 <p class="validation"></p>
 1644 
 <p class="validation"></p>
1645 
 </div>
 1645 
 </div>
1646
1646

+ 10
- 10
build/emd_Me_Me.html View File

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3 
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 <head>
4 
-<!-- 2022-03-22 Tue 10:52 -->
4 
+<!-- 2022-03-24 Thu 08:42 -->
5 
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6 
 <meta name="viewport" content="width=device-width, initial-scale=1">
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 <meta name="viewport" content="width=device-width, initial-scale=1">
7 
 <title>Pre-Quantum Electrodynamics</title>
 7 
 <title>Pre-Quantum Electrodynamics</title>
1293 
 </summary>
 1293 
 </summary>
1294 
 <ul>
 1294 
 <ul>
1295 
 <li>
 1295 
 <li>
1296 
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
1296 
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
1297
1297
1298 
 </li>
 1298 
 </li>
1299
1299
1616 
 <p>
 1616 
 <p>
1617 
 Full set of equations for the electromagnetic field:
 1617 
 Full set of equations for the electromagnetic field:
1618 
 </p>
 1618 
 </p>
1619 
-<div class="core div" id="org71429ce">
1619 
+<div class="core div" id="org96eda60">
1620 
 <p>
 1620 
 <p>
1621 
 <b>Maxwell's equations</b> <i>(in vacuum)</i>
 1621 
 <b>Maxwell's equations</b> <i>(in vacuum)</i>
1622 
 </p>
 1622 
 </p>
1623 
-<div class="eqlabel" id="org92aa36d">
1623 
+<div class="eqlabel" id="org99bc512">
1624 
 <p>
 1624 
 <p>
1625 
 <a id="Max_vac"></a><a href="./emd_Me_Me.html#Max_vac"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
 1625 
 <a id="Max_vac"></a><a href="./emd_Me_Me.html#Max_vac"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
1626 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
 1626 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
1627 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 1627 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
1628 
 </svg></a>
 1628 
 </svg></a>
1629 
 </p>
 1629 
 </p>
1630 
-<div class="alteqlabels" id="orgd8ea0a7">
1630 
+<div class="alteqlabels" id="org0385504">
1631
1631
1632 
 </div>
 1632 
 </div>
1633
1633
1644 
 <p>
 1644 
 <p>
1645 
 Complement:
 1645 
 Complement:
1646 
 </p>
 1646 
 </p>
1647 
-<div class="core div" id="org93d1ad6">
1647 
+<div class="core div" id="org8bd62bd">
1648 
 <p>
 1648 
 <p>
1649 
 Force law <a href="./ems_ms_lf_pc.html#LorFo">LorFo</a>
 1649 
 Force law <a href="./ems_ms_lf_pc.html#LorFo">LorFo</a>
1650 
 \[
 1650 
 \[
1667 
 <p>
 1667 
 <p>
1668 
 Better way of writing:  all fields on left, all sources on right,
 1668 
 Better way of writing:  all fields on left, all sources on right,
1669 
 </p>
 1669 
 </p>
1670 
-<div class="core div" id="org82c9083">
1671 
-<div class="eqlabel" id="org1583626">
1670 
+<div class="core div" id="org3b3efc0">
1671 
+<div class="eqlabel" id="orgaa87be2">
1672 
 <p>
 1672 
 <p>
1673 
 <a id="Max_vac_s"></a><a href="./emd_Me_Me.html#Max_vac_s"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
 1673 
 <a id="Max_vac_s"></a><a href="./emd_Me_Me.html#Max_vac_s"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
1674 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
 1674 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
1675 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 1675 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
1676 
 </svg></a>
 1676 
 </svg></a>
1677 
 </p>
 1677 
 </p>
1678 
-<div class="alteqlabels" id="orgfc0a16c">
1678 
+<div class="alteqlabels" id="org3e69b1d">
1679 
 <ul class="org-ul">
 1679 
 <ul class="org-ul">
1680 
 <li>Gr (7.42)</li>
 1680 
 <li>Gr (7.42)</li>
1681 
 </ul>
 1681 
 </ul>
1713 
 </div>
 1713 
 </div>
1714 
 <div id="postamble" class="status">
 1714 
 <div id="postamble" class="status">
1715 
 <p class="author">Author: Jean-Sébastien Caux</p>
 1715 
 <p class="author">Author: Jean-Sébastien Caux</p>
1716 
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
1716 
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
1717 
 <p class="validation"></p>
 1717 
 <p class="validation"></p>
1718 
 </div>
 1718 
 </div>
1719
1719

+ 9
- 9
build/emd_Me_dc.html View File

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+<!-- 2022-03-24 Thu 08:42 -->
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 <meta name="viewport" content="width=device-width, initial-scale=1">
7 
 <title>Pre-Quantum Electrodynamics</title>
 7 
 <title>Pre-Quantum Electrodynamics</title>
1293 
 </summary>
 1293 
 </summary>
1294 
 <ul>
 1294 
 <ul>
1295 
 <li>
 1295 
 <li>
1296 
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
1296 
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
1297
1297
1298 
 </li>
 1298 
 </li>
1299
1299
1622 
 \]
 1622 
 \]
1623 
 The extra term would thus be eliminated if we were to put
 1623 
 The extra term would thus be eliminated if we were to put
1624 
 </p>
 1624 
 </p>
1625 
-<div class="core div" id="orgfb244bd">
1626 
-<div class="eqlabel" id="org02e358a">
1625 
+<div class="core div" id="org65d0a3c">
1626 
+<div class="eqlabel" id="org2343c92">
1627 
 <p>
 1627 
 <p>
1628 
 <a id="AmpMax"></a><a href="./emd_Me_dc.html#AmpMax"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
 1628 
 <a id="AmpMax"></a><a href="./emd_Me_dc.html#AmpMax"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
1629 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
 1629 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
1630 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 1630 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
1631 
 </svg></a>
 1631 
 </svg></a>
1632 
 </p>
 1632 
 </p>
1633 
-<div class="alteqlabels" id="orgf266507">
1633 
+<div class="alteqlabels" id="org09fe122">
1634 
 <ul class="org-ul">
 1634 
 <ul class="org-ul">
1635 
 <li>Gr (7.36)</li>
 1635 
 <li>Gr (7.36)</li>
1636 
 </ul>
 1636 
 </ul>
1659 
 <p>
 1659 
 <p>
1660 
 Maxwell baptized this term the
 1660 
 Maxwell baptized this term the
1661 
 </p>
 1661 
 </p>
1662 
-<div class="core div" id="orgb3e1688">
1662 
+<div class="core div" id="org9a1c650">
1663 
 <p>
 1663 
 <p>
1664 
 <b>Displacement current</b>
 1664 
 <b>Displacement current</b>
1665 
 </p>
 1665 
 </p>
1666 
-<div class="eqlabel" id="org5bc6ac9">
1666 
+<div class="eqlabel" id="orgea96ca5">
1667 
 <p>
 1667 
 <p>
1668 
 <a id="Jd"></a><a href="./emd_Me_dc.html#Jd"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
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 <a id="Jd"></a><a href="./emd_Me_dc.html#Jd"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
1669 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
 1669 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
1670 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 1670 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
1671 
 </svg></a>
 1671 
 </svg></a>
1672 
 </p>
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 </p>
1673 
-<div class="alteqlabels" id="org2273d93">
1673 
+<div class="alteqlabels" id="org147727a">
1674 
 <ul class="org-ul">
 1674 
 <ul class="org-ul">
1675 
 <li>Gr (7.37)</li>
 1675 
 <li>Gr (7.37)</li>
1676 
 </ul>
 1676 
 </ul>
1724 
 </div>
 1724 
 </div>
1725 
 <div id="postamble" class="status">
 1725 
 <div id="postamble" class="status">
1726 
 <p class="author">Author: Jean-Sébastien Caux</p>
 1726 
 <p class="author">Author: Jean-Sébastien Caux</p>
1727 
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
1727 
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
1728 
 <p class="validation"></p>
 1728 
 <p class="validation"></p>
1729 
 </div>
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 </div>
1730
1730

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build/emd_Me_ebM.html View File

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 <title>Pre-Quantum Electrodynamics</title>
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 <title>Pre-Quantum Electrodynamics</title>
1293 
 </summary>
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 </summary>
1294 
 <ul>
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 <ul>
1295 
 <li>
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 <li>
1296 
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
1296 
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
1297
1297
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 </li>
1299
1299
1630 
 \]
 1630 
 \]
1631 
 But:  try same with \((iv)\):
 1631 
 But:  try same with \((iv)\):
1632 
 </p>
 1632 
 </p>
1633 
-<div class="eqlabel" id="org1332a90">
1633 
+<div class="eqlabel" id="org5adad0c">
1634 
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 <p>
1635 
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1636 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
 1636 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
1637 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 1637 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
1638 
 </svg></a>
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 </svg></a>
1639 
 </p>
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1640 
-<div class="alteqlabels" id="orgc919b58">
1640 
+<div class="alteqlabels" id="orga04de46">
1641 
 <ul class="org-ul">
 1641 
 <ul class="org-ul">
1642 
 <li>Gr (7.35)</li>
 1642 
 <li>Gr (7.35)</li>
1643 
 </ul>
 1643 
 </ul>
1682 
 </div>
 1682 
 </div>
1683 
 <div id="postamble" class="status">
 1683 
 <div id="postamble" class="status">
1684 
 <p class="author">Author: Jean-Sébastien Caux</p>
 1684 
 <p class="author">Author: Jean-Sébastien Caux</p>
1685 
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
1685 
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
1686 
 <p class="validation"></p>
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1687 
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1688
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+ 3
- 3
build/emd_Me_mc.html View File

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 <title>Pre-Quantum Electrodynamics</title>
1293 
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1294 
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 <ul>
1295 
 <li>
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 <li>
1296 
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
1296 
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
1297
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1663 
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1664 
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 <div id="postamble" class="status">
1665 
 <p class="author">Author: Jean-Sébastien Caux</p>
 1665 
 <p class="author">Author: Jean-Sébastien Caux</p>
1666 
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
1666 
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
1667 
 <p class="validation"></p>
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build/emd_ce.html View File

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 <title>Pre-Quantum Electrodynamics</title>
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 <title>Pre-Quantum Electrodynamics</title>
1293 
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 </summary>
1294 
 <ul>
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 <ul>
1295 
 <li>
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 <li>
1296 
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
1296 
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
1297
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1614 
 </svg></a><span class="headline-id">emd.ce</span></h3>
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1615
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1616 
 <div class="outline-text-3" id="text-emd_ce">
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1617 
-<details class="prereq" id="org4aea2a7">
1618 
-<summary id="orgbb42f82">
1617 
+<details class="prereq" id="orgbcfd9aa">
1618 
+<summary id="orgfd4a1b6">
1619 
 Prerequisites
 1619 
 Prerequisites
1620 
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1621 
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 <ul class="org-ul">
1623 
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1625
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-<details class="objectives" id="orgacf1d30">
1627 
-<summary id="org560d61d">
1626 
+<details class="objectives" id="orgb58d097">
1627 
+<summary id="org5cd5f85">
1628 
 Objectives
 1628 
 Objectives
1629 
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1630 
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1662 
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1663 
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 1663 
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1664 
 <p class="author">Author: Jean-Sébastien Caux</p>
 1664 
 <p class="author">Author: Jean-Sébastien Caux</p>
1665 
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
1665 
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
1666 
 <p class="validation"></p>
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build/emd_ce_amom.html View File

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 <title>Pre-Quantum Electrodynamics</title>
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 <title>Pre-Quantum Electrodynamics</title>
1293 
 </summary>
 1293 
 </summary>
1294 
 <ul>
 1294 
 <ul>
1295 
 <li>
 1295 
 <li>
1296 
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
1296 
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
1297
1297
1298 
 </li>
 1298 
 </li>
1299
1299
1616 
 <p>
 1616 
 <p>
1617 
 The angular momentum of EM fields is directly given by
 1617 
 The angular momentum of EM fields is directly given by
1618 
 </p>
 1618 
 </p>
1619 
-<div class="main div" id="org8982815">
1619 
+<div class="main div" id="orgc2d5343">
1620 
 <p>
 1620 
 <p>
1621 
 <b>Angular momentum of EM fields</b>
 1621 
 <b>Angular momentum of EM fields</b>
1622 
 </p>
 1622 
 </p>
1623 
-<div class="eqlabel" id="org8297ce4">
1623 
+<div class="eqlabel" id="orgd4d0682">
1624 
 <p>
 1624 
 <p>
1625 
 <a id="lrxg"></a><a href="./emd_ce_amom.html#lrxg"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
 1625 
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1626 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
 1626 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
1627 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 1627 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
1628 
 </svg></a>
 1628 
 </svg></a>
1629 
 </p>
 1629 
 </p>
1630 
-<div class="alteqlabels" id="orgc1dccb2">
1630 
+<div class="alteqlabels" id="orgf246c58">
1631
1631
1632 
 </div>
 1632 
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1633
1633
1661 
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 1661 
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1662 
 <div id="postamble" class="status">
 1662 
 <div id="postamble" class="status">
1663 
 <p class="author">Author: Jean-Sébastien Caux</p>
 1663 
 <p class="author">Author: Jean-Sébastien Caux</p>
1664 
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
1664 
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
1665 
 <p class="validation"></p>
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+ 4
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build/emd_ce_ce.html View File

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 <title>Pre-Quantum Electrodynamics</title>
1293 
 </summary>
 1293 
 </summary>
1294 
 <ul>
 1294 
 <ul>
1295 
 <li>
 1295 
 <li>
1296 
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
1296 
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
1297
1297
1298 
 </li>
 1298 
 </li>
1299
1299
1635 
 \]
 1635 
 \]
1636 
 Since this is true for any volume, we have (re)derived the
 1636 
 Since this is true for any volume, we have (re)derived the
1637 
 </p>
 1637 
 </p>
1638 
-<div class="core div" id="org1d21244">
1638 
+<div class="core div" id="orgc746662">
1639 
 <p>
 1639 
 <p>
1640 
 <b>Continuity equation</b> <a href="./ems_ms_ce.html#conteq">conteq</a>
 1640 
 <b>Continuity equation</b> <a href="./ems_ms_ce.html#conteq">conteq</a>
1641 
 \[
 1641 
 \[
1675 
 </div>
 1675 
 </div>
1676 
 <div id="postamble" class="status">
 1676 
 <div id="postamble" class="status">
1677 
 <p class="author">Author: Jean-Sébastien Caux</p>
 1677 
 <p class="author">Author: Jean-Sébastien Caux</p>
1678 
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
1678 
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
1679 
 <p class="validation"></p>
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 <p class="validation"></p>
1680 
 </div>
 1680 
 </div>
1681
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+ 9
- 9
build/emd_ce_mom.html View File

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 7 
 <title>Pre-Quantum Electrodynamics</title>
1293 
 </summary>
 1293 
 </summary>
1294 
 <ul>
 1294 
 <ul>
1295 
 <li>
 1295 
 <li>
1296 
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
1296 
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
1297
1297
1298 
 </li>
 1298 
 </li>
1299
1299
1628 
 <p>
 1628 
 <p>
1629 
 This is thus simply a conservation law for momentum, with
 1629 
 This is thus simply a conservation law for momentum, with
1630 
 </p>
 1630 
 </p>
1631 
-<div class="main div" id="orgbd3d67d">
1631 
+<div class="main div" id="org9032358">
1632 
 <p>
 1632 
 <p>
1633 
 <b>Momentum density in the EM fields</b>
 1633 
 <b>Momentum density in the EM fields</b>
1634 
 </p>
 1634 
 </p>
1635 
-<div class="eqlabel" id="org2b66251">
1635 
+<div class="eqlabel" id="org0649d73">
1636 
 <p>
 1636 
 <p>
1637 
 <a id="gExB"></a><a href="./emd_ce_mom.html#gExB"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
 1637 
 <a id="gExB"></a><a href="./emd_ce_mom.html#gExB"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
1638 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
 1638 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
1639 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 1639 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
1640 
 </svg></a>
 1640 
 </svg></a>
1641 
 </p>
 1641 
 </p>
1642 
-<div class="alteqlabels" id="org006aaa0">
1642 
+<div class="alteqlabels" id="org7dc7b00">
1643
1643
1644 
 </div>
 1644 
 </div>
1645
1645
1655 
 <p>
 1655 
 <p>
1656 
 In a region in which the mechanical momentum is not changing due to external influences, we then have the
 1656 
 In a region in which the mechanical momentum is not changing due to external influences, we then have the
1657 
 </p>
 1657 
 </p>
1658 
-<div class="main div" id="orgd647d42">
1658 
+<div class="main div" id="org72dfdb8">
1659 
 <p>
 1659 
 <p>
1660 
 <b>Continuity equation for EM momentum</b>
 1660 
 <b>Continuity equation for EM momentum</b>
1661 
 </p>
 1661 
 </p>
1662 
-<div class="eqlabel" id="org84364f8">
1662 
+<div class="eqlabel" id="org89a6b5f">
1663 
 <p>
 1663 
 <p>
1664 
 <a id="contg"></a><a href="./emd_ce_mom.html#contg"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
 1664 
 <a id="contg"></a><a href="./emd_ce_mom.html#contg"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
1665 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
 1665 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
1666 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 1666 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
1667 
 </svg></a>
 1667 
 </svg></a>
1668 
 </p>
 1668 
 </p>
1669 
-<div class="alteqlabels" id="org03c5d23">
1669 
+<div class="alteqlabels" id="orgd3a1580">
1670
1670
1671 
 </div>
 1671 
 </div>
1672
1672
1699 
 </div>
 1699 
 </div>
1700 
 <div id="postamble" class="status">
 1700 
 <div id="postamble" class="status">
1701 
 <p class="author">Author: Jean-Sébastien Caux</p>
 1701 
 <p class="author">Author: Jean-Sébastien Caux</p>
1702 
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
1702 
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
1703 
 <p class="validation"></p>
 1703 
 <p class="validation"></p>
1704 
 </div>
 1704 
 </div>
1705
1705

+ 12
- 12
build/emd_ce_mst.html View File

1 
 <!DOCTYPE html>
 1 
 <!DOCTYPE html>
2 
 <html lang="en">
 2 
 <html lang="en">
3 
 <head>
 3 
 <head>
4 
-<!-- 2022-03-22 Tue 10:52 -->
4 
+<!-- 2022-03-24 Thu 08:42 -->
5 
 <meta charset="utf-8">
 5 
 <meta charset="utf-8">
6 
 <meta name="viewport" content="width=device-width, initial-scale=1">
 6 
 <meta name="viewport" content="width=device-width, initial-scale=1">
7 
 <title>Pre-Quantum Electrodynamics</title>
 7 
 <title>Pre-Quantum Electrodynamics</title>
1293 
 </summary>
 1293 
 </summary>
1294 
 <ul>
 1294 
 <ul>
1295 
 <li>
 1295 
 <li>
1296 
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
1296 
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
1297
1297
1298 
 </li>
 1298 
 </li>
1299
1299
1667 
 <p>
 1667 
 <p>
1668 
 This expression can be greatly simplified by introducing the
 1668 
 This expression can be greatly simplified by introducing the
1669 
 </p>
 1669 
 </p>
1670 
-<div class="main div" id="org63be843">
1670 
+<div class="main div" id="orge483101">
1671 
 <p>
 1671 
 <p>
1672 
 <b>Maxwell stress tensor</b>
 1672 
 <b>Maxwell stress tensor</b>
1673 
 </p>
 1673 
 </p>
1674 
-<div class="eqlabel" id="org7c75f9d">
1674 
+<div class="eqlabel" id="org42e9f16">
1675 
 <p>
 1675 
 <p>
1676 
 <a id="MaxST"></a><a href="./emd_ce_mst.html#MaxST"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
 1676 
 <a id="MaxST"></a><a href="./emd_ce_mst.html#MaxST"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
1677 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
 1677 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
1678 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 1678 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
1679 
 </svg></a>
 1679 
 </svg></a>
1680 
 </p>
 1680 
 </p>
1681 
-<div class="alteqlabels" id="orgd84a618">
1681 
+<div class="alteqlabels" id="orgf3e9098">
1682
1682
1683 
 </div>
 1683 
 </div>
1684
1684
1699 
 <p>
 1699 
 <p>
1700 
 We then obtain the
 1700 
 We then obtain the
1701 
 </p>
 1701 
 </p>
1702 
-<div class="main div" id="orgfeaab67">
1702 
+<div class="main div" id="org3664d29">
1703 
 <p>
 1703 
 <p>
1704 
 <b>EM force per unit volume</b>
 1704 
 <b>EM force per unit volume</b>
1705 
 </p>
 1705 
 </p>
1706 
-<div class="eqlabel" id="org9fc5057">
1706 
+<div class="eqlabel" id="org6136353">
1707 
 <p>
 1707 
 <p>
1708 
 <a id="fT"></a><a href="./emd_ce_mst.html#fT"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
 1708 
 <a id="fT"></a><a href="./emd_ce_mst.html#fT"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
1709 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
 1709 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
1710 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 1710 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
1711 
 </svg></a>
 1711 
 </svg></a>
1712 
 </p>
 1712 
 </p>
1713 
-<div class="alteqlabels" id="orgecbfdae">
1713 
+<div class="alteqlabels" id="org7273a9f">
1714
1714
1715 
 </div>
 1715 
 </div>
1716
1716
1726 
 <p>
 1726 
 <p>
1727 
 where \({\boldsymbol S}\) is the Poynting vector. Integrating, we obtain the
 1727 
 where \({\boldsymbol S}\) is the Poynting vector. Integrating, we obtain the
1728 
 </p>
 1728 
 </p>
1729 
-<div class="main div" id="org86829bd">
1729 
+<div class="main div" id="org2a4f340">
1730 
 <p>
 1730 
 <p>
1731 
 <b>Total force on charges in volume</b>
 1731 
 <b>Total force on charges in volume</b>
1732 
 </p>
 1732 
 </p>
1733 
-<div class="eqlabel" id="org2370cf3">
1733 
+<div class="eqlabel" id="org0298272">
1734 
 <p>
 1734 
 <p>
1735 
 <a id="totFo"></a><a href="./emd_ce_mst.html#totFo"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
 1735 
 <a id="totFo"></a><a href="./emd_ce_mst.html#totFo"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
1736 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
 1736 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
1737 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 1737 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
1738 
 </svg></a>
 1738 
 </svg></a>
1739 
 </p>
 1739 
 </p>
1740 
-<div class="alteqlabels" id="orgc55376c">
1740 
+<div class="alteqlabels" id="org1024eff">
1741
1741
1742 
 </div>
 1742 
 </div>
1743
1743
1770 
 </div>
 1770 
 </div>
1771 
 <div id="postamble" class="status">
 1771 
 <div id="postamble" class="status">
1772 
 <p class="author">Author: Jean-Sébastien Caux</p>
 1772 
 <p class="author">Author: Jean-Sébastien Caux</p>
1773 
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
1773 
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
1774 
 <p class="validation"></p>
 1774 
 <p class="validation"></p>
1775 
 </div>
 1775 
 </div>
1776
1776

+ 21
- 21
build/emd_ce_poy.html View File

1 
 <!DOCTYPE html>
 1 
 <!DOCTYPE html>
2 
 <html lang="en">
 2 
 <html lang="en">
3 
 <head>
 3 
 <head>
4 
-<!-- 2022-03-22 Tue 10:52 -->
4 
+<!-- 2022-03-24 Thu 08:42 -->
5 
 <meta charset="utf-8">
 5 
 <meta charset="utf-8">
6 
 <meta name="viewport" content="width=device-width, initial-scale=1">
 6 
 <meta name="viewport" content="width=device-width, initial-scale=1">
7 
 <title>Pre-Quantum Electrodynamics</title>
 7 
 <title>Pre-Quantum Electrodynamics</title>
1293 
 </summary>
 1293 
 </summary>
1294 
 <ul>
 1294 
 <ul>
1295 
 <li>
 1295 
 <li>
1296 
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
1296 
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
1297
1297
1298 
 </li>
 1298 
 </li>
1299
1299
1636 
 Really, we're looking at a small volume element \(d\tau\) carrying charge \(\rho d\tau\), moving
 1636 
 Really, we're looking at a small volume element \(d\tau\) carrying charge \(\rho d\tau\), moving
1637 
 at velocity \({\bf v}\) such that \({\bf J} = \rho {\bf v}\).  Thus,
 1637 
 at velocity \({\bf v}\) such that \({\bf J} = \rho {\bf v}\).  Thus,
1638 
 </p>
 1638 
 </p>
1639 
-<div class="eqlabel" id="orge2567ac">
1639 
+<div class="eqlabel" id="org0c693e0">
1640 
 <p>
 1640 
 <p>
1641 
 <a id="dWdt_intEJ"></a><a href="./emd_ce_poy.html#dWdt_intEJ"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
 1641 
 <a id="dWdt_intEJ"></a><a href="./emd_ce_poy.html#dWdt_intEJ"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
1642 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
 1642 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
1643 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 1643 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
1644 
 </svg></a>
 1644 
 </svg></a>
1645 
 </p>
 1645 
 </p>
1646 
-<div class="alteqlabels" id="org4d05a80">
1646 
+<div class="alteqlabels" id="orge34a4b7">
1647 
 <ul class="org-ul">
 1647 
 <ul class="org-ul">
1648 
 <li>Gr (8.6)</li>
 1648 
 <li>Gr (8.6)</li>
1649 
 </ul>
 1649 
 </ul>
1683 
 Substituting this in <a href="./emd_ce_poy.html#dWdt_intEJ">dWdt_intEJ</a> and using the divergence theorem,
 1683 
 Substituting this in <a href="./emd_ce_poy.html#dWdt_intEJ">dWdt_intEJ</a> and using the divergence theorem,
1684 
 we obtain
 1684 
 we obtain
1685 
 </p>
 1685 
 </p>
1686 
-<div class="main div" id="org36db96e">
1686 
+<div class="main div" id="orgb7d7869">
1687 
 <p>
 1687 
 <p>
1688 
 <b>Poynting's theorem</b>
 1688 
 <b>Poynting's theorem</b>
1689 
 </p>
 1689 
 </p>
1690 
-<div class="eqlabel" id="org21ce6b8">
1690 
+<div class="eqlabel" id="org1a4b16b">
1691 
 <p>
 1691 
 <p>
1692 
 <a id="👉Thm"></a><a href="./emd_ce_poy.html#👉Thm"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
 1692 
 <a id="👉Thm"></a><a href="./emd_ce_poy.html#👉Thm"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
1693 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
 1693 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
1694 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 1694 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
1695 
 </svg></a>
 1695 
 </svg></a>
1696 
 </p>
 1696 
 </p>
1697 
-<div class="alteqlabels" id="org09a112b">
1697 
+<div class="alteqlabels" id="org4feadff">
1698 
 <ul class="org-ul">
 1698 
 <ul class="org-ul">
1699 
 <li>Gr (8.9)</li>
 1699 
 <li>Gr (8.9)</li>
1700 
 </ul>
 1700 
 </ul>
1720 
 <p>
 1720 
 <p>
1721 
 Energy per unit time, per unit area carried by EM fields: given by the
 1721 
 Energy per unit time, per unit area carried by EM fields: given by the
1722 
 </p>
 1722 
 </p>
1723 
-<div class="core div" id="org0bf3f6c">
1723 
+<div class="core div" id="orgdc56ce9">
1724 
 <p>
 1724 
 <p>
1725 
 <b>Poynting vector</b>
 1725 
 <b>Poynting vector</b>
1726 
 </p>
 1726 
 </p>
1727 
-<div class="eqlabel" id="org327095e">
1727 
+<div class="eqlabel" id="orga61d997">
1728 
 <p>
 1728 
 <p>
1729 
 <a id="PoyntingVec"></a><a href="./emd_ce_poy.html#PoyntingVec"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
 1729 
 <a id="PoyntingVec"></a><a href="./emd_ce_poy.html#PoyntingVec"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
1730 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
 1730 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
1731 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 1731 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
1732 
 </svg></a>
 1732 
 </svg></a>
1733 
 </p>
 1733 
 </p>
1734 
-<div class="alteqlabels" id="org7684a8e">
1734 
+<div class="alteqlabels" id="orgb7a4cb9">
1735 
 <ul class="org-ul">
 1735 
 <ul class="org-ul">
1736 
 <li>Gr (8.10)</li>
 1736 
 <li>Gr (8.10)</li>
1737 
 </ul>
 1737 
 </ul>
1750 
 <p>
 1750 
 <p>
1751 
 We can thus express Poynting's theorem more compactly:
 1751 
 We can thus express Poynting's theorem more compactly:
1752 
 </p>
 1752 
 </p>
1753 
-<div class="core div" id="org4255191">
1753 
+<div class="core div" id="orgd48d57f">
1754 
 <p>
 1754 
 <p>
1755 
 <b>Poynting's theorem</b> (integral form)
 1755 
 <b>Poynting's theorem</b> (integral form)
1756 
 </p>
 1756 
 </p>
1757 
-<div class="eqlabel" id="orgd0524d3">
1757 
+<div class="eqlabel" id="org32c9daf">
1758 
 <p>
 1758 
 <p>
1759 
 <a id="PoyntingThm_int"></a><a href="./emd_ce_poy.html#PoyntingThm_int"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
 1759 
 <a id="PoyntingThm_int"></a><a href="./emd_ce_poy.html#PoyntingThm_int"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
1760 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
 1760 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
1761 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 1761 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
1762 
 </svg></a>
 1762 
 </svg></a>
1763 
 </p>
 1763 
 </p>
1764 
-<div class="alteqlabels" id="org8acaa16">
1764 
+<div class="alteqlabels" id="org59d2761">
1765 
 <ul class="org-ul">
 1765 
 <ul class="org-ul">
1766 
 <li>Gr (8.11)</li>
 1766 
 <li>Gr (8.11)</li>
1767 
 </ul>
 1767 
 </ul>
1780 
 <p>
 1780 
 <p>
1781 
 where we have defined the total
 1781 
 where we have defined the total
1782 
 </p>
 1782 
 </p>
1783 
-<div class="core div" id="org85e77e2">
1783 
+<div class="core div" id="org5e10531">
1784 
 <p>
 1784 
 <p>
1785 
 <b>Energy in electromagnetic fields</b>
 1785 
 <b>Energy in electromagnetic fields</b>
1786 
 </p>
 1786 
 </p>
1787 
-<div class="eqlabel" id="org7d4ae3d">
1787 
+<div class="eqlabel" id="orgad6f50f">
1788 
 <p>
 1788 
 <p>
1789 
 <a id="Uem"></a><a href="./emd_ce_poy.html#Uem"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
 1789 
 <a id="Uem"></a><a href="./emd_ce_poy.html#Uem"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
1790 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
 1790 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
1791 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 1791 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
1792 
 </svg></a>
 1792 
 </svg></a>
1793 
 </p>
 1793 
 </p>
1794 
-<div class="alteqlabels" id="org7a55647">
1794 
+<div class="alteqlabels" id="orga3df7bc">
1795 
 <ul class="org-ul">
 1795 
 <ul class="org-ul">
1796 
 <li>Gr (8.5)</li>
 1796 
 <li>Gr (8.5)</li>
1797 
 </ul>
 1797 
 </ul>
1820 
 \]
 1820 
 \]
1821 
 so we get the
 1821 
 so we get the
1822 
 </p>
 1822 
 </p>
1823 
-<div class="core div" id="orgbdb096d">
1823 
+<div class="core div" id="orgb7a11e9">
1824 
 <p>
 1824 
 <p>
1825 
 <b>Poynting theorem</b> (differential form)
 1825 
 <b>Poynting theorem</b> (differential form)
1826 
 </p>
 1826 
 </p>
1827 
-<div class="eqlabel" id="org9c56948">
1827 
+<div class="eqlabel" id="orga2e5c79">
1828 
 <p>
 1828 
 <p>
1829 
 <a id="PoyntingThm"></a><a href="./emd_ce_poy.html#PoyntingThm"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
 1829 
 <a id="PoyntingThm"></a><a href="./emd_ce_poy.html#PoyntingThm"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
1830 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
 1830 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
1831 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 1831 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
1832 
 </svg></a>
 1832 
 </svg></a>
1833 
 </p>
 1833 
 </p>
1834 
-<div class="alteqlabels" id="orgdfe3994">
1834 
+<div class="alteqlabels" id="org0cf780d">
1835 
 <ul class="org-ul">
 1835 
 <ul class="org-ul">
1836 
 <li>Gr (8.14)</li>
 1836 
 <li>Gr (8.14)</li>
1837 
 </ul>
 1837 
 </ul>
1854
1854
1855
1855
1856
1856
1857 
-<div class="example div" id="org15b725b">
1857 
+<div class="example div" id="org1083447">
1858 
 <p>
 1858 
 <p>
1859 
 <b>Example:  Joule heating</b>
 1859 
 <b>Example:  Joule heating</b>
1860 
 </p>
 1860 
 </p>
1911 
 </div>
 1911 
 </div>
1912 
 <div id="postamble" class="status">
 1912 
 <div id="postamble" class="status">
1913 
 <p class="author">Author: Jean-Sébastien Caux</p>
 1913 
 <p class="author">Author: Jean-Sébastien Caux</p>
1914 
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
1914 
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
1915 
 <p class="validation"></p>
 1915 
 <p class="validation"></p>
1916 
 </div>
 1916 
 </div>
1917
1917

+ 7
- 7
build/emd_emw.html View File

1 
 <!DOCTYPE html>
 1 
 <!DOCTYPE html>
2 
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 <html lang="en">
3 
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4 
-<!-- 2022-03-22 Tue 10:52 -->
4 
+<!-- 2022-03-24 Thu 08:42 -->
5 
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 <meta charset="utf-8">
6 
 <meta name="viewport" content="width=device-width, initial-scale=1">
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 <meta name="viewport" content="width=device-width, initial-scale=1">
7 
 <title>Pre-Quantum Electrodynamics</title>
 7 
 <title>Pre-Quantum Electrodynamics</title>
1293 
 </summary>
 1293 
 </summary>
1294 
 <ul>
 1294 
 <ul>
1295 
 <li>
 1295 
 <li>
1296 
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
1296 
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
1297
1297
1298 
 </li>
 1298 
 </li>
1299
1299
1614 
 </svg></a><span class="headline-id">emd.emw</span></h3>
 1614 
 </svg></a><span class="headline-id">emd.emw</span></h3>
1615
1615
1616 
 <div class="outline-text-3" id="text-emd_emw">
 1616 
 <div class="outline-text-3" id="text-emd_emw">
1617 
-<details class="prereq" id="org17a8cef">
1618 
-<summary id="org45e360a">
1617 
+<details class="prereq" id="org92d8d0c">
1618 
+<summary id="orgb97228e">
1619 
 Prerequisites
 1619 
 Prerequisites
1620 
 </summary>
 1620 
 </summary>
1621 
 <ul class="org-ul">
 1621 
 <ul class="org-ul">
1624 
 </ul>
 1624 
 </ul>
1625 
 </details>
 1625 
 </details>
1626
1626
1627 
-<details class="objectives" id="org91615eb">
1628 
-<summary id="orgec366bf">
1627 
+<details class="objectives" id="org5c24096">
1628 
+<summary id="orge645495">
1629 
 Objectives
 1629 
 Objectives
1630 
 </summary>
 1630 
 </summary>
1631 
 <ul class="org-ul">
 1631 
 <ul class="org-ul">
1659 
 </div>
 1659 
 </div>
1660 
 <div id="postamble" class="status">
 1660 
 <div id="postamble" class="status">
1661 
 <p class="author">Author: Jean-Sébastien Caux</p>
 1661 
 <p class="author">Author: Jean-Sébastien Caux</p>
1662 
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
1662 
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
1663 
 <p class="validation"></p>
 1663 
 <p class="validation"></p>
1664 
 </div>
 1664 
 </div>
1665
1665

+ 7
- 7
build/emd_emw_ep.html View File

1 
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2 
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3 
 <head>
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4 
-<!-- 2022-03-22 Tue 10:52 -->
4 
+<!-- 2022-03-24 Thu 08:42 -->
5 
 <meta charset="utf-8">
 5 
 <meta charset="utf-8">
6 
 <meta name="viewport" content="width=device-width, initial-scale=1">
 6 
 <meta name="viewport" content="width=device-width, initial-scale=1">
7 
 <title>Pre-Quantum Electrodynamics</title>
 7 
 <title>Pre-Quantum Electrodynamics</title>
1293 
 </summary>
 1293 
 </summary>
1294 
 <ul>
 1294 
 <ul>
1295 
 <li>
 1295 
 <li>
1296 
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
1296 
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
1297
1297
1298 
 </li>
 1298 
 </li>
1299
1299
1644 
 \]
 1644 
 \]
1645 
 or more succinctly:
 1645 
 or more succinctly:
1646 
 </p>
 1646 
 </p>
1647 
-<div class="main div" id="orgdf4b8bc">
1647 
+<div class="main div" id="orga5c9575">
1648 
 <p>
 1648 
 <p>
1649 
 <b>Poynting vector of a monochromatic EM wave</b>
 1649 
 <b>Poynting vector of a monochromatic EM wave</b>
1650 
 </p>
 1650 
 </p>
1651 
-<div class="eqlabel" id="org3913519">
1651 
+<div class="eqlabel" id="org72a5a32">
1652 
 <p>
 1652 
 <p>
1653 
 <a id="Poynting_mpw"></a><a href="./emd_emw_ep.html#Poynting_mpw"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
 1653 
 <a id="Poynting_mpw"></a><a href="./emd_emw_ep.html#Poynting_mpw"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
1654 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
 1654 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
1655 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 1655 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
1656 
 </svg></a>
 1656 
 </svg></a>
1657 
 </p>
 1657 
 </p>
1658 
-<div class="alteqlabels" id="org8b59092">
1658 
+<div class="alteqlabels" id="org7e5d7a7">
1659 
 <ul class="org-ul">
 1659 
 <ul class="org-ul">
1660 
 <li>Gr (9.57)</li>
 1660 
 <li>Gr (9.57)</li>
1661 
 </ul>
 1661 
 </ul>
1678 
 <p>
 1678 
 <p>
1679 
 Similary, we get the
 1679 
 Similary, we get the
1680 
 </p>
 1680 
 </p>
1681 
-<div class="main div" id="org21912bb">
1681 
+<div class="main div" id="orgd6eada9">
1682 
 <p>
 1682 
 <p>
1683 
 <b>Momentum density of a monochromatic EM wave</b>
 1683 
 <b>Momentum density of a monochromatic EM wave</b>
1684 
 \[
 1684 
 \[
1729 
 </div>
 1729 
 </div>
1730 
 <div id="postamble" class="status">
 1730 
 <div id="postamble" class="status">
1731 
 <p class="author">Author: Jean-Sébastien Caux</p>
 1731 
 <p class="author">Author: Jean-Sébastien Caux</p>
1732 
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
1732 
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
1733 
 <p class="validation"></p>
 1733 
 <p class="validation"></p>
1734 
 </div>
 1734 
 </div>
1735
1735

+ 8
- 8
build/emd_emw_mpw.html View File

1 
 <!DOCTYPE html>
 1 
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2 
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 2 
 <html lang="en">
3 
 <head>
 3 
 <head>
4 
-<!-- 2022-03-22 Tue 10:52 -->
4 
+<!-- 2022-03-24 Thu 08:42 -->
5 
 <meta charset="utf-8">
 5 
 <meta charset="utf-8">
6 
 <meta name="viewport" content="width=device-width, initial-scale=1">
 6 
 <meta name="viewport" content="width=device-width, initial-scale=1">
7 
 <title>Pre-Quantum Electrodynamics</title>
 7 
 <title>Pre-Quantum Electrodynamics</title>
1293 
 </summary>
 1293 
 </summary>
1294 
 <ul>
 1294 
 <ul>
1295 
 <li>
 1295 
 <li>
1296 
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
1296 
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
1297
1297
1298 
 </li>
 1298 
 </li>
1299
1299
1636 
 \]
 1636 
 \]
1637 
 so \({\bf E}\) and \({\bf B}\) are mutually perpendicular, and
 1637 
 so \({\bf E}\) and \({\bf B}\) are mutually perpendicular, and
1638 
 </p>
 1638 
 </p>
1639 
-<div class="eqlabel" id="org619c73f">
1639 
+<div class="eqlabel" id="org44bb1e2">
1640 
 <p>
 1640 
 <p>
1641 
 <a id="EBmpw"></a><a href="./emd_emw_mpw.html#EBmpw"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
 1641 
 <a id="EBmpw"></a><a href="./emd_emw_mpw.html#EBmpw"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
1642 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
 1642 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
1643 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 1643 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
1644 
 </svg></a>
 1644 
 </svg></a>
1645 
 </p>
 1645 
 </p>
1646 
-<div class="alteqlabels" id="orgaad096d">
1646 
+<div class="alteqlabels" id="org0064233">
1647 
 <ul class="org-ul">
 1647 
 <ul class="org-ul">
1648 
 <li>Gr (9.47)</li>
 1648 
 <li>Gr (9.47)</li>
1649 
 </ul>
 1649 
 </ul>
1662 
 Generalizing to propagation in the direction of an arbitrary wavevector
 1662 
 Generalizing to propagation in the direction of an arbitrary wavevector
1663 
 \({\boldsymbol k}\) and (transverse) polarization vector \(\hat{\boldsymbol n}\), we have the
 1663 
 \({\boldsymbol k}\) and (transverse) polarization vector \(\hat{\boldsymbol n}\), we have the
1664 
 </p>
 1664 
 </p>
1665 
-<div class="core div" id="org9c77e17">
1665 
+<div class="core div" id="org83aeece">
1666 
 <p>
 1666 
 <p>
1667 
 <b>E and B fields for a monochromatic EM plane wave</b>
 1667 
 <b>E and B fields for a monochromatic EM plane wave</b>
1668 
 </p>
 1668 
 </p>
1669 
-<div class="eqlabel" id="org54506e2">
1669 
+<div class="eqlabel" id="org82e71ea">
1670 
 <p>
 1670 
 <p>
1671 
 <a id="mpw"></a><a href="./emd_emw_mpw.html#mpw"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
 1671 
 <a id="mpw"></a><a href="./emd_emw_mpw.html#mpw"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
1672 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
 1672 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
1673 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 1673 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
1674 
 </svg></a>
 1674 
 </svg></a>
1675 
 </p>
 1675 
 </p>
1676 
-<div class="alteqlabels" id="orgb384c79">
1676 
+<div class="alteqlabels" id="orgb1b901e">
1677 
 <ul class="org-ul">
 1677 
 <ul class="org-ul">
1678 
 <li>Gr (9.49)</li>
 1678 
 <li>Gr (9.49)</li>
1679 
 </ul>
 1679 
 </ul>
1724 
 </div>
 1724 
 </div>
1725 
 <div id="postamble" class="status">
 1725 
 <div id="postamble" class="status">
1726 
 <p class="author">Author: Jean-Sébastien Caux</p>
 1726 
 <p class="author">Author: Jean-Sébastien Caux</p>
1727 
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
1727 
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
1728 
 <p class="validation"></p>
 1728 
 <p class="validation"></p>
1729 
 </div>
 1729 
 </div>
1730
1730

+ 6
- 6
build/emd_emw_we.html View File

1 
 <!DOCTYPE html>
 1 
 <!DOCTYPE html>
2 
 <html lang="en">
 2 
 <html lang="en">
3 
 <head>
 3 
 <head>
4 
-<!-- 2022-03-22 Tue 10:52 -->
4 
+<!-- 2022-03-24 Thu 08:42 -->
5 
 <meta charset="utf-8">
 5 
 <meta charset="utf-8">
6 
 <meta name="viewport" content="width=device-width, initial-scale=1">
 6 
 <meta name="viewport" content="width=device-width, initial-scale=1">
7 
 <title>Pre-Quantum Electrodynamics</title>
 7 
 <title>Pre-Quantum Electrodynamics</title>
1293 
 </summary>
 1293 
 </summary>
1294 
 <ul>
 1294 
 <ul>
1295 
 <li>
 1295 
 <li>
1296 
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
1296 
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
1297
1297
1298 
 </li>
 1298 
 </li>
1299
1299
1641 
 Since \({\boldsymbol \nabla} \cdot {\bf E} = 0\) and \({\boldsymbol \nabla} \cdot {\bf B} = 0\),
 1641 
 Since \({\boldsymbol \nabla} \cdot {\bf E} = 0\) and \({\boldsymbol \nabla} \cdot {\bf B} = 0\),
1642 
 we get the
 1642 
 we get the
1643 
 </p>
 1643 
 </p>
1644 
-<div class="core div" id="org0b3ebdc">
1644 
+<div class="core div" id="orge19d256">
1645 
 <p>
 1645 
 <p>
1646 
 <b>Wave equations for electric and magnetic fields in vacuum</b>
 1646 
 <b>Wave equations for electric and magnetic fields in vacuum</b>
1647 
 </p>
 1647 
 </p>
1648 
-<div class="eqlabel" id="orge465a34">
1648 
+<div class="eqlabel" id="orgff19c15">
1649 
 <p>
 1649 
 <p>
1650 
 <a id="WaveEq"></a><a href="./emd_emw_we.html#WaveEq"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
 1650 
 <a id="WaveEq"></a><a href="./emd_emw_we.html#WaveEq"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
1651 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
 1651 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
1652 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 1652 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
1653 
 </svg></a>
 1653 
 </svg></a>
1654 
 </p>
 1654 
 </p>
1655 
-<div class="alteqlabels" id="org3ff5ea0">
1655 
+<div class="alteqlabels" id="orga8c7165">
1656 
 <ul class="org-ul">
 1656 
 <ul class="org-ul">
1657 
 <li>Gr (9.41)</li>
 1657 
 <li>Gr (9.41)</li>
1658 
 </ul>
 1658 
 </ul>
1714 
 </div>
 1714 
 </div>
1715 
 <div id="postamble" class="status">
 1715 
 <div id="postamble" class="status">
1716 
 <p class="author">Author: Jean-Sébastien Caux</p>
 1716 
 <p class="author">Author: Jean-Sébastien Caux</p>
1717 
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
1717 
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
1718 
 <p class="validation"></p>
 1718 
 <p class="validation"></p>
1719 
 </div>
 1719 
 </div>
1720
1720

+ 3
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build/emdm.html View File

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7 
 <title>Pre-Quantum Electrodynamics</title>
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 <title>Pre-Quantum Electrodynamics</title>
1293 
 </summary>
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 </summary>
1294 
 <ul>
 1294 
 <ul>
1295 
 <li>
 1295 
 <li>
1296 
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
1296 
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
1297
1297
1298 
 </li>
 1298 
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1299
1299
1638 
 </div>
 1638 
 </div>
1639 
 <div id="postamble" class="status">
 1639 
 <div id="postamble" class="status">
1640 
 <p class="author">Author: Jean-Sébastien Caux</p>
 1640 
 <p class="author">Author: Jean-Sébastien Caux</p>
1641 
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
1641 
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
1642 
 <p class="validation"></p>
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1643 
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build/emdm_Me.html View File

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3 
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4 
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+<!-- 2022-03-24 Thu 08:42 -->
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6 
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 <meta name="viewport" content="width=device-width, initial-scale=1">
7 
 <title>Pre-Quantum Electrodynamics</title>
 7 
 <title>Pre-Quantum Electrodynamics</title>
1293 
 </summary>
 1293 
 </summary>
1294 
 <ul>
 1294 
 <ul>
1295 
 <li>
 1295 
 <li>
1296 
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
1296 
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
1297
1297
1298 
 </li>
 1298 
 </li>
1299
1299
1638 
 </div>
 1638 
 </div>
1639 
 <div id="postamble" class="status">
 1639 
 <div id="postamble" class="status">
1640 
 <p class="author">Author: Jean-Sébastien Caux</p>
 1640 
 <p class="author">Author: Jean-Sébastien Caux</p>
1641 
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
1641 
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
1642 
 <p class="validation"></p>
 1642 
 <p class="validation"></p>
1643 
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 </div>
1644
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build/emdm_Me_Mem.html View File

1 
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2 
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3 
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4 
-<!-- 2022-03-22 Tue 10:52 -->
4 
+<!-- 2022-03-24 Thu 08:42 -->
5 
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 <meta charset="utf-8">
6 
 <meta name="viewport" content="width=device-width, initial-scale=1">
 6 
 <meta name="viewport" content="width=device-width, initial-scale=1">
7 
 <title>Pre-Quantum Electrodynamics</title>
 7 
 <title>Pre-Quantum Electrodynamics</title>
1293 
 </summary>
 1293 
 </summary>
1294 
 <ul>
 1294 
 <ul>
1295 
 <li>
 1295 
 <li>
1296 
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
1296 
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
1297
1297
1298 
 </li>
 1298 
 </li>
1299
1299
1648 
 \]
 1648 
 \]
1649 
 We therefore have the
 1649 
 We therefore have the
1650 
 </p>
 1650 
 </p>
1651 
-<div class="core div" id="org64396a0">
1651 
+<div class="core div" id="orgc00904a">
1652 
 <p>
 1652 
 <p>
1653 
 <b>Polarization current density</b>
 1653 
 <b>Polarization current density</b>
1654 
 </p>
 1654 
 </p>
1655 
-<div class="eqlabel" id="orgf37fc4f">
1655 
+<div class="eqlabel" id="org3742df8">
1656 
 <p>
 1656 
 <p>
1657 
 <a id="Jp"></a><a href="./emdm_Me_Mem.html#Jp"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
 1657 
 <a id="Jp"></a><a href="./emdm_Me_Mem.html#Jp"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
1658 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
 1658 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
1659 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 1659 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
1660 
 </svg></a>
 1660 
 </svg></a>
1661 
 </p>
 1661 
 </p>
1662 
-<div class="alteqlabels" id="org12af1ad">
1662 
+<div class="alteqlabels" id="org6073635">
1663 
 <ul class="org-ul">
 1663 
 <ul class="org-ul">
1664 
 <li>Gr (7.48)</li>
 1664 
 <li>Gr (7.48)</li>
1665 
 </ul>
 1665 
 </ul>
1683 
 polarization changes).  We can check consistency with the continuity equation
 1683 
 polarization changes).  We can check consistency with the continuity equation
1684 
 associated to the conservation of bound charges:
 1684 
 associated to the conservation of bound charges:
1685 
 </p>
 1685 
 </p>
1686 
-<aside id="org0322793">
1686 
+<aside id="orgff2c75f">
1687 
 <p>
 1687 
 <p>
1688 
 Note the unfortunate labelling: it would have been nicer to have \(\rho_b\) be the charge associated to current \({\boldsymbol J}_b\) but this is not the common convention.
 1688 
 Note the unfortunate labelling: it would have been nicer to have \(\rho_b\) be the charge associated to current \({\boldsymbol J}_b\) but this is not the common convention.
1689 
 </p>
 1689 
 </p>
1705 
 In view of this:  total charge density can be separated into 2 parts,
 1705 
 In view of this:  total charge density can be separated into 2 parts,
1706 
 <b>free</b> and <b>bound</b>:
 1706 
 <b>free</b> and <b>bound</b>:
1707 
 </p>
 1707 
 </p>
1708 
-<div class="main div" id="org56027a6">
1709 
-<div class="eqlabel" id="org6fd2aed">
1708 
+<div class="main div" id="org7866a36">
1709 
+<div class="eqlabel" id="orge94a27e">
1710 
 <p>
 1710 
 <p>
1711 
 <a id="rhofb"></a><a href="./emdm_Me_Mem.html#rhofb"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
 1711 
 <a id="rhofb"></a><a href="./emdm_Me_Mem.html#rhofb"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
1712 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
 1712 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
1713 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 1713 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
1714 
 </svg></a>
 1714 
 </svg></a>
1715 
 </p>
 1715 
 </p>
1716 
-<div class="alteqlabels" id="org9e03f13">
1716 
+<div class="alteqlabels" id="orgbb91da6">
1717 
 <ul class="org-ul">
 1717 
 <ul class="org-ul">
1718 
 <li>Gr (7.49)</li>
 1718 
 <li>Gr (7.49)</li>
1719 
 </ul>
 1719 
 </ul>
1733 
 and current can be separated into three parts, <b>free</b>, <b>bound</b> and
 1733 
 and current can be separated into three parts, <b>free</b>, <b>bound</b> and
1734 
 <b>polarization</b>:
 1734 
 <b>polarization</b>:
1735 
 </p>
 1735 
 </p>
1736 
-<div class="main div" id="org96443a3">
1737 
-<div class="eqlabel" id="orga6b8e4a">
1736 
+<div class="main div" id="org765eeee">
1737 
+<div class="eqlabel" id="org49803b2">
1738 
 <p>
 1738 
 <p>
1739 
 <a id="Jfbp"></a><a href="./emdm_Me_Mem.html#Jfbp"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
 1739 
 <a id="Jfbp"></a><a href="./emdm_Me_Mem.html#Jfbp"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
1740 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
 1740 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
1741 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 1741 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
1742 
 </svg></a>
 1742 
 </svg></a>
1743 
 </p>
 1743 
 </p>
1744 
-<div class="alteqlabels" id="orgddcfaf9">
1744 
+<div class="alteqlabels" id="orgc87ffc7">
1745 
 <ul class="org-ul">
 1745 
 <ul class="org-ul">
1746 
 <li>Gr (7.50)</li>
 1746 
 <li>Gr (7.50)</li>
1747 
 </ul>
 1747 
 </ul>
1767 
 \]
 1767 
 \]
1768 
 where (as in static case)
 1768 
 where (as in static case)
1769 
 </p>
 1769 
 </p>
1770 
-<div class="core div" id="orgdbd92f1">
1770 
+<div class="core div" id="org91a1e38">
1771 
 <p>
 1771 
 <p>
1772 
 \[
 1772 
 \[
1773 
 {\bf D} \equiv \varepsilon_0 {\bf E} + {\bf P}
 1773 
 {\bf D} \equiv \varepsilon_0 {\bf E} + {\bf P}
1788 
 \]
 1788 
 \]
1789 
 where as before
 1789 
 where as before
1790 
 </p>
 1790 
 </p>
1791 
-<div class="core div" id="org7839f4c">
1791 
+<div class="core div" id="org0c2e84f">
1792 
 <p>
 1792 
 <p>
1793 
 \[
 1793 
 \[
1794 
 {\bf H} \equiv \frac{1}{\mu_0} {\bf B} - {\bf M}
 1794 
 {\bf H} \equiv \frac{1}{\mu_0} {\bf B} - {\bf M}
1806 
 <p>
 1806 
 <p>
1807 
 In terms of free charges and currents, we thus get
 1807 
 In terms of free charges and currents, we thus get
1808 
 </p>
 1808 
 </p>
1809 
-<div class="core div" id="org6597738">
1809 
+<div class="core div" id="orgeeb0b35">
1810 
 <p>
 1810 
 <p>
1811 
 <b>Maxwell's equations</b> <i>(in matter)</i>
 1811 
 <b>Maxwell's equations</b> <i>(in matter)</i>
1812 
 </p>
 1812 
 </p>
1813 
-<div class="eqlabel" id="orgffcbbe9">
1813 
+<div class="eqlabel" id="orgb9e6675">
1814 
 <p>
 1814 
 <p>
1815 
 <a id="Max_mat"></a><a href="./emdm_Me_Mem.html#Max_mat"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
 1815 
 <a id="Max_mat"></a><a href="./emdm_Me_Mem.html#Max_mat"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
1816 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
 1816 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
1817 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 1817 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
1818 
 </svg></a>
 1818 
 </svg></a>
1819 
 </p>
 1819 
 </p>
1820 
-<div class="alteqlabels" id="org5c6c62d">
1820 
+<div class="alteqlabels" id="org6367cef">
1821 
 <ul class="org-ul">
 1821 
 <ul class="org-ul">
1822 
 <li>Gr (7.55)</li>
 1822 
 <li>Gr (7.55)</li>
1823 
 </ul>
 1823 
 </ul>
1847 
 in terms of \({\bf E}\) and \({\bf B}\).
 1847 
 in terms of \({\bf E}\) and \({\bf B}\).
1848 
 For the restricted case of linear media:
 1848 
 For the restricted case of linear media:
1849 
 </p>
 1849 
 </p>
1850 
-<div class="main div" id="org2d4f8dd">
1851 
-<div class="eqlabel" id="org03c06a4">
1850 
+<div class="main div" id="orgd78e0b5">
1851 
+<div class="eqlabel" id="org86e1a29">
1852 
 <p>
 1852 
 <p>
1853 
 <a id="consrel"></a><a href="./emdm_Me_Mem.html#consrel"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
 1853 
 <a id="consrel"></a><a href="./emdm_Me_Mem.html#consrel"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
1854 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
 1854 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
1855 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 1855 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
1856 
 </svg></a>
 1856 
 </svg></a>
1857 
 </p>
 1857 
 </p>
1858 
-<div class="alteqlabels" id="org45b4fff">
1858 
+<div class="alteqlabels" id="org7ea2c8c">
1859 
 <ul class="org-ul">
 1859 
 <ul class="org-ul">
1860 
 <li>Gr (7.56,7.57)</li>
 1860 
 <li>Gr (7.56,7.57)</li>
1861 
 </ul>
 1861 
 </ul>
1898 
 </div>
 1898 
 </div>
1899 
 <div id="postamble" class="status">
 1899 
 <div id="postamble" class="status">
1900 
 <p class="author">Author: Jean-Sébastien Caux</p>
 1900 
 <p class="author">Author: Jean-Sébastien Caux</p>
1901 
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
1901 
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
1902 
 <p class="validation"></p>
 1902 
 <p class="validation"></p>
1903 
 </div>
 1903 
 </div>
1904
1904

+ 19
- 19
build/emdm_Me_bc.html View File

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+<!-- 2022-03-24 Thu 08:42 -->
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 <meta name="viewport" content="width=device-width, initial-scale=1">
7 
 <title>Pre-Quantum Electrodynamics</title>
 7 
 <title>Pre-Quantum Electrodynamics</title>
1293 
 </summary>
 1293 
 </summary>
1294 
 <ul>
 1294 
 <ul>
1295 
 <li>
 1295 
 <li>
1296 
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
1296 
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
1297
1297
1298 
 </li>
 1298 
 </li>
1299
1299
1616 
 <p>
 1616 
 <p>
1617 
 Discontinuities between different media, deduced from
 1617 
 Discontinuities between different media, deduced from
1618 
 </p>
 1618 
 </p>
1619 
-<div class="core div" id="orgb7aedd2">
1619 
+<div class="core div" id="org876a60b">
1620 
 <p>
 1620 
 <p>
1621 
 <b>Maxwell's equations</b> <i>(in matter)</i>, <i>integral form</i>
 1621 
 <b>Maxwell's equations</b> <i>(in matter)</i>, <i>integral form</i>
1622 
 </p>
 1622 
 </p>
1623 
-<div class="eqlabel" id="org6c267cc">
1623 
+<div class="eqlabel" id="orga776629">
1624 
 <p>
 1624 
 <p>
1625 
 <a id="Max_mat_int"></a><a href="./emdm_Me_bc.html#Max_mat_int"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
 1625 
 <a id="Max_mat_int"></a><a href="./emdm_Me_bc.html#Max_mat_int"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
1626 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
 1626 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
1627 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 1627 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
1628 
 </svg></a>
 1628 
 </svg></a>
1629 
 </p>
 1629 
 </p>
1630 
-<div class="alteqlabels" id="org8952960">
1630 
+<div class="alteqlabels" id="org6c05186">
1631
1631
1632 
 </div>
 1632 
 </div>
1633
1633
1645 
 Applying \((i)\) to wafer-thin Gaussian pillbox straddling boundary between 2 materials:
 1645 
 Applying \((i)\) to wafer-thin Gaussian pillbox straddling boundary between 2 materials:
1646 
 \({\bf D}_1 \cdot {\bf a} - {\bf D}_2 \cdot {\bf a} = \sigma_f a\) so
 1646 
 \({\bf D}_1 \cdot {\bf a} - {\bf D}_2 \cdot {\bf a} = \sigma_f a\) so
1647 
 </p>
 1647 
 </p>
1648 
-<div class="main div" id="orgf92353e">
1649 
-<div class="eqlabel" id="orgb9a9a3d">
1648 
+<div class="main div" id="org8d20540">
1649 
+<div class="eqlabel" id="org7926d65">
1650 
 <p>
 1650 
 <p>
1651 
 <a id="Ddisc"></a><a href="./emdm_Me_bc.html#Ddisc"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
 1651 
 <a id="Ddisc"></a><a href="./emdm_Me_bc.html#Ddisc"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
1652 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
 1652 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
1653 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 1653 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
1654 
 </svg></a>
 1654 
 </svg></a>
1655 
 </p>
 1655 
 </p>
1656 
-<div class="alteqlabels" id="orga6c409d">
1656 
+<div class="alteqlabels" id="orge1fcf9c">
1657 
 <ul class="org-ul">
 1657 
 <ul class="org-ul">
1658 
 <li>Gr (7.60)</li>
 1658 
 <li>Gr (7.60)</li>
1659 
 </ul>
 1659 
 </ul>
1672 
 <p>
 1672 
 <p>
1673 
 Same reasoning applied to \((ii)\) gives <a href="./ems_ms_vp_mbc.html#Bdisc">Bdisc</a>
 1673 
 Same reasoning applied to \((ii)\) gives <a href="./ems_ms_vp_mbc.html#Bdisc">Bdisc</a>
1674 
 </p>
 1674 
 </p>
1675 
-<div class="main div" id="orga22be6d">
1676 
-<div class="eqlabel" id="orge0d8321">
1677 
-<div class="alteqlabels" id="orgb94a831">
1675 
+<div class="main div" id="orgfa3145b">
1676 
+<div class="eqlabel" id="orgddc00f3">
1677 
+<div class="alteqlabels" id="org80b4003">
1678
1678
1679 
 </div>
 1679 
 </div>
1680
1680
1690 
 For \((iii)\):  Amperian loop straddling surface:  \({\bf E}_1 \cdot {\bf l} - {\bf E}_2 \cdot {\bf l} =
 1690 
 For \((iii)\):  Amperian loop straddling surface:  \({\bf E}_1 \cdot {\bf l} - {\bf E}_2 \cdot {\bf l} =
1691 
 -\frac{d}{dt} \int_{\cal S} {\bf B} \cdot d{\bf a}\).  Limit of small loop:  flux vanishes, therefore
 1691 
 -\frac{d}{dt} \int_{\cal S} {\bf B} \cdot d{\bf a}\).  Limit of small loop:  flux vanishes, therefore
1692 
 </p>
 1692 
 </p>
1693 
-<div class="main div" id="org55a1d42">
1693 
+<div class="main div" id="org2dd2bbb">
1694 
 <p>
 1694 
 <p>
1695 
 \[
 1695 
 \[
1696 
 {\bf E}_1^{\parallel} - {\bf E}_2^{\parallel} = 0
 1696 
 {\bf E}_1^{\parallel} - {\bf E}_2^{\parallel} = 0
1704 
 \(I_{f_{enc}} = {\bf K}_f \cdot (\hat{\bf n} \times {\bf l}) = ({\bf K}_f \times \hat{\bf n}) \cdot {\bf l}\)
 1704 
 \(I_{f_{enc}} = {\bf K}_f \cdot (\hat{\bf n} \times {\bf l}) = ({\bf K}_f \times \hat{\bf n}) \cdot {\bf l}\)
1705 
 and thus (as we got before in <a href="./emsm_msm_H_A.html#Hdisc">Hdisc</a>)
 1705 
 and thus (as we got before in <a href="./emsm_msm_H_A.html#Hdisc">Hdisc</a>)
1706 
 </p>
 1706 
 </p>
1707 
-<div class="main div" id="org4a2ee70">
1707 
+<div class="main div" id="orgd223e2f">
1708 
 <p>
 1708 
 <p>
1709 
 \[
 1709 
 \[
1710 
 {\bf H}_1^{\parallel} - {\bf H}_2^{\parallel} = {\bf K}_f \times \hat{\bf n}
 1710 
 {\bf H}_1^{\parallel} - {\bf H}_2^{\parallel} = {\bf K}_f \times \hat{\bf n}
1720 
 <p>
 1720 
 <p>
1721 
 In case of linear media:  can be expressed in terms of \({\bf E}\) and \({\bf B}\) alone:
 1721 
 In case of linear media:  can be expressed in terms of \({\bf E}\) and \({\bf B}\) alone:
1722 
 </p>
 1722 
 </p>
1723 
-<div class="main div" id="org9e90e47">
1724 
-<div class="eqlabel" id="org8bbc727">
1723 
+<div class="main div" id="orgaafde6e">
1724 
+<div class="eqlabel" id="orge514e83">
1725 
 <p>
 1725 
 <p>
1726 
 <a id="disc_lm"></a><a href="./emdm_Me_bc.html#disc_lm"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
 1726 
 <a id="disc_lm"></a><a href="./emdm_Me_bc.html#disc_lm"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
1727 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
 1727 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
1728 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 1728 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
1729 
 </svg></a>
 1729 
 </svg></a>
1730 
 </p>
 1730 
 </p>
1731 
-<div class="alteqlabels" id="orga51b616">
1731 
+<div class="alteqlabels" id="org786e6ec">
1732 
 <ul class="org-ul">
 1732 
 <ul class="org-ul">
1733 
 <li>Gr (7.64)</li>
 1733 
 <li>Gr (7.64)</li>
1734 
 </ul>
 1734 
 </ul>
1748 
 <p>
 1748 
 <p>
1749 
 If there is no free charge and no free current at boundary:
 1749 
 If there is no free charge and no free current at boundary:
1750 
 </p>
 1750 
 </p>
1751 
-<div class="eqlabel" id="orgf07dc3e">
1751 
+<div class="eqlabel" id="orga74521d">
1752 
 <p>
 1752 
 <p>
1753 
 <a id="disc_nfc"></a><a href="./emdm_Me_bc.html#disc_nfc"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
 1753 
 <a id="disc_nfc"></a><a href="./emdm_Me_bc.html#disc_nfc"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
1754 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
 1754 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
1755 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 1755 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
1756 
 </svg></a>
 1756 
 </svg></a>
1757 
 </p>
 1757 
 </p>
1758 
-<div class="alteqlabels" id="orgdd74046">
1758 
+<div class="alteqlabels" id="orgac68624">
1759 
 <ul class="org-ul">
 1759 
 <ul class="org-ul">
1760 
 <li>Gr (7.64)</li>
 1760 
 <li>Gr (7.64)</li>
1761 
 </ul>
 1761 
 </ul>
1792 
 </div>
 1792 
 </div>
1793 
 <div id="postamble" class="status">
 1793 
 <div id="postamble" class="status">
1794 
 <p class="author">Author: Jean-Sébastien Caux</p>
 1794 
 <p class="author">Author: Jean-Sébastien Caux</p>
1795 
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
1795 
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
1796 
 <p class="validation"></p>
 1796 
 <p class="validation"></p>
1797 
 </div>
 1797 
 </div>
1798
1798

+ 7
- 7
build/emdm_emwm.html View File

1 
 <!DOCTYPE html>
 1 
 <!DOCTYPE html>
2 
 <html lang="en">
 2 
 <html lang="en">
3 
 <head>
 3 
 <head>
4 
-<!-- 2022-03-22 Tue 10:52 -->
4 
+<!-- 2022-03-24 Thu 08:42 -->
5 
 <meta charset="utf-8">
 5 
 <meta charset="utf-8">
6 
 <meta name="viewport" content="width=device-width, initial-scale=1">
 6 
 <meta name="viewport" content="width=device-width, initial-scale=1">
7 
 <title>Pre-Quantum Electrodynamics</title>
 7 
 <title>Pre-Quantum Electrodynamics</title>
1293 
 </summary>
 1293 
 </summary>
1294 
 <ul>
 1294 
 <ul>
1295 
 <li>
 1295 
 <li>
1296 
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
1296 
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
1297
1297
1298 
 </li>
 1298 
 </li>
1299
1299
1614 
 </svg></a><span class="headline-id">emdm.emwm</span></h3>
 1614 
 </svg></a><span class="headline-id">emdm.emwm</span></h3>
1615
1615
1616 
 <div class="outline-text-3" id="text-emdm_emwm">
 1616 
 <div class="outline-text-3" id="text-emdm_emwm">
1617 
-<details class="prereq" id="org5c9f997">
1618 
-<summary id="orgcac0ec5">
1617 
+<details class="prereq" id="org499ec58">
1618 
+<summary id="org504cdbb">
1619 
 Prerequisites
 1619 
 Prerequisites
1620 
 </summary>
 1620 
 </summary>
1621 
 <ul class="org-ul">
 1621 
 <ul class="org-ul">
1625 
 </ul>
 1625 
 </ul>
1626 
 </details>
 1626 
 </details>
1627
1627
1628 
-<details class="objectives" id="orgde042c7">
1629 
-<summary id="org6ca3c40">
1628 
+<details class="objectives" id="org76e4576">
1629 
+<summary id="org77d80f7">
1630 
 Objectives
 1630 
 Objectives
1631 
 </summary>
 1631 
 </summary>
1632 
 <ul class="org-ul">
 1632 
 <ul class="org-ul">
1666 
 </div>
 1666 
 </div>
1667 
 <div id="postamble" class="status">
 1667 
 <div id="postamble" class="status">
1668 
 <p class="author">Author: Jean-Sébastien Caux</p>
 1668 
 <p class="author">Author: Jean-Sébastien Caux</p>
1669 
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
1669 
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
1670 
 <p class="validation"></p>
 1670 
 <p class="validation"></p>
1671 
 </div>
 1671 
 </div>
1672
1672

+ 3
- 3
build/emdm_emwm_ad.html View File

1 
 <!DOCTYPE html>
 1 
 <!DOCTYPE html>
2 
 <html lang="en">
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 <html lang="en">
3 
 <head>
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 <head>
4 
-<!-- 2022-03-22 Tue 10:52 -->
4 
+<!-- 2022-03-24 Thu 08:42 -->
5 
 <meta charset="utf-8">
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 <meta charset="utf-8">
6 
 <meta name="viewport" content="width=device-width, initial-scale=1">
 6 
 <meta name="viewport" content="width=device-width, initial-scale=1">
7 
 <title>Pre-Quantum Electrodynamics</title>
 7 
 <title>Pre-Quantum Electrodynamics</title>
1293 
 </summary>
 1293 
 </summary>
1294 
 <ul>
 1294 
 <ul>
1295 
 <li>
 1295 
 <li>
1296 
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
1296 
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
1297
1297
1298 
 </li>
 1298 
 </li>
1299
1299
1637 
 </div>
 1637 
 </div>
1638 
 <div id="postamble" class="status">
 1638 
 <div id="postamble" class="status">
1639 
 <p class="author">Author: Jean-Sébastien Caux</p>
 1639 
 <p class="author">Author: Jean-Sébastien Caux</p>
1640 
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
1640 
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
1641 
 <p class="validation"></p>
 1641 
 <p class="validation"></p>
1642 
 </div>
 1642 
 </div>
1643
1643

+ 3
- 3
build/emdm_emwm_ad_c.html View File

1 
 <!DOCTYPE html>
 1 
 <!DOCTYPE html>
2 
 <html lang="en">
 2 
 <html lang="en">
3 
 <head>
 3 
 <head>
4 
-<!-- 2022-03-22 Tue 10:52 -->
4 
+<!-- 2022-03-24 Thu 08:42 -->
5 
 <meta charset="utf-8">
 5 
 <meta charset="utf-8">
6 
 <meta name="viewport" content="width=device-width, initial-scale=1">
 6 
 <meta name="viewport" content="width=device-width, initial-scale=1">
7 
 <title>Pre-Quantum Electrodynamics</title>
 7 
 <title>Pre-Quantum Electrodynamics</title>
1293 
 </summary>
 1293 
 </summary>
1294 
 <ul>
 1294 
 <ul>
1295 
 <li>
 1295 
 <li>
1296 
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
1296 
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
1297
1297
1298 
 </li>
 1298 
 </li>
1299
1299
1733 
 </div>
 1733 
 </div>
1734 
 <div id="postamble" class="status">
 1734 
 <div id="postamble" class="status">
1735 
 <p class="author">Author: Jean-Sébastien Caux</p>
 1735 
 <p class="author">Author: Jean-Sébastien Caux</p>
1736 
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
1736 
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
1737 
 <p class="validation"></p>
 1737 
 <p class="validation"></p>
1738 
 </div>
 1738 
 </div>
1739
1739

+ 9
- 9
build/emdm_emwm_plm.html View File

1 
 <!DOCTYPE html>
 1 
 <!DOCTYPE html>
2 
 <html lang="en">
 2 
 <html lang="en">
3 
 <head>
 3 
 <head>
4 
-<!-- 2022-03-22 Tue 10:52 -->
4 
+<!-- 2022-03-24 Thu 08:42 -->
5 
 <meta charset="utf-8">
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 <meta charset="utf-8">
6 
 <meta name="viewport" content="width=device-width, initial-scale=1">
 6 
 <meta name="viewport" content="width=device-width, initial-scale=1">
7 
 <title>Pre-Quantum Electrodynamics</title>
 7 
 <title>Pre-Quantum Electrodynamics</title>
1293 
 </summary>
 1293 
 </summary>
1294 
 <ul>
 1294 
 <ul>
1295 
 <li>
 1295 
 <li>
1296 
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
1296 
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
1297
1297
1298 
 </li>
 1298 
 </li>
1299
1299
1632 
 \]
 1632 
 \]
1633 
 If the medium is homogeneous (no spatial dependence of \(\varepsilon\) or \(\mu\)),
 1633 
 If the medium is homogeneous (no spatial dependence of \(\varepsilon\) or \(\mu\)),
1634 
 </p>
 1634 
 </p>
1635 
-<div class="main div" id="org3abedbf">
1636 
-<div class="eqlabel" id="org6c3c992">
1635 
+<div class="main div" id="orgead2b1c">
1636 
+<div class="eqlabel" id="org9916855">
1637 
 <p>
 1637 
 <p>
1638 
 <a id="Max_lh"></a><a href="./emdm_emwm_plm.html#Max_lh"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
 1638 
 <a id="Max_lh"></a><a href="./emdm_emwm_plm.html#Max_lh"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
1639 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
 1639 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
1640 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 1640 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
1641 
 </svg></a>
 1641 
 </svg></a>
1642 
 </p>
 1642 
 </p>
1643 
-<div class="alteqlabels" id="org4747e62">
1643 
+<div class="alteqlabels" id="org5111273">
1644 
 <ul class="org-ul">
 1644 
 <ul class="org-ul">
1645 
 <li>Gr (9.65)</li>
 1645 
 <li>Gr (9.65)</li>
1646 
 </ul>
 1646 
 </ul>
1669 
 \]
 1669 
 \]
1670 
 where the index of refraction of the material is defined as
 1670 
 where the index of refraction of the material is defined as
1671 
 </p>
 1671 
 </p>
1672 
-<div class="main div" id="org92a77a7">
1672 
+<div class="main div" id="org5237a1a">
1673 
 <p>
 1673 
 <p>
1674 
 <b>Index of refraction</b>
 1674 
 <b>Index of refraction</b>
1675 
 </p>
 1675 
 </p>
1676 
-<div class="eqlabel" id="orgb3ac891">
1676 
+<div class="eqlabel" id="org6cb7362">
1677 
 <p>
 1677 
 <p>
1678 
 <a id="n"></a><a href="./emdm_emwm_plm.html#n"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
 1678 
 <a id="n"></a><a href="./emdm_emwm_plm.html#n"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
1679 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
 1679 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
1680 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 1680 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
1681 
 </svg></a>
 1681 
 </svg></a>
1682 
 </p>
 1682 
 </p>
1683 
-<div class="alteqlabels" id="orge10b1d5">
1683 
+<div class="alteqlabels" id="orgc12f464">
1684 
 <ul class="org-ul">
 1684 
 <ul class="org-ul">
1685 
 <li>Gr (9.69)</li>
 1685 
 <li>Gr (9.69)</li>
1686 
 </ul>
 1686 
 </ul>
1743 
 </div>
 1743 
 </div>
1744 
 <div id="postamble" class="status">
 1744 
 <div id="postamble" class="status">
1745 
 <p class="author">Author: Jean-Sébastien Caux</p>
 1745 
 <p class="author">Author: Jean-Sébastien Caux</p>
1746 
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
1746 
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
1747 
 <p class="validation"></p>
 1747 
 <p class="validation"></p>
1748 
 </div>
 1748 
 </div>
1749
1749

+ 3
- 3
build/emdm_emwm_refl.html View File

1 
 <!DOCTYPE html>
 1 
 <!DOCTYPE html>
2 
 <html lang="en">
 2 
 <html lang="en">
3 
 <head>
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 <head>
4 
-<!-- 2022-03-22 Tue 10:52 -->
4 
+<!-- 2022-03-24 Thu 08:42 -->
5 
 <meta charset="utf-8">
 5 
 <meta charset="utf-8">
6 
 <meta name="viewport" content="width=device-width, initial-scale=1">
 6 
 <meta name="viewport" content="width=device-width, initial-scale=1">
7 
 <title>Pre-Quantum Electrodynamics</title>
 7 
 <title>Pre-Quantum Electrodynamics</title>
1293 
 </summary>
 1293 
 </summary>
1294 
 <ul>
 1294 
 <ul>
1295 
 <li>
 1295 
 <li>
1296 
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
1296 
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
1297
1297
1298 
 </li>
 1298 
 </li>
1299
1299
1649 
 </div>
 1649 
 </div>
1650 
 <div id="postamble" class="status">
 1650 
 <div id="postamble" class="status">
1651 
 <p class="author">Author: Jean-Sébastien Caux</p>
 1651 
 <p class="author">Author: Jean-Sébastien Caux</p>
1652 
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
1652 
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
1653 
 <p class="validation"></p>
 1653 
 <p class="validation"></p>
1654 
 </div>
 1654 
 </div>
1655
1655

+ 5
- 5
build/emdm_emwm_refl_ni.html View File

1 
 <!DOCTYPE html>
 1 
 <!DOCTYPE html>
2 
 <html lang="en">
 2 
 <html lang="en">
3 
 <head>
 3 
 <head>
4 
-<!-- 2022-03-22 Tue 10:52 -->
4 
+<!-- 2022-03-24 Thu 08:42 -->
5 
 <meta charset="utf-8">
 5 
 <meta charset="utf-8">
6 
 <meta name="viewport" content="width=device-width, initial-scale=1">
 6 
 <meta name="viewport" content="width=device-width, initial-scale=1">
7 
 <title>Pre-Quantum Electrodynamics</title>
 7 
 <title>Pre-Quantum Electrodynamics</title>
1293 
 </summary>
 1293 
 </summary>
1294 
 <ul>
 1294 
 <ul>
1295 
 <li>
 1295 
 <li>
1296 
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
1296 
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
1297
1297
1298 
 </li>
 1298 
 </li>
1299
1299
1671 
 Solving these coupled equations, we can write
 1671 
 Solving these coupled equations, we can write
1672 
 outgoing amplitudes in terms of incident ones:
 1672 
 outgoing amplitudes in terms of incident ones:
1673 
 </p>
 1673 
 </p>
1674 
-<div class="eqlabel" id="org0451818">
1674 
+<div class="eqlabel" id="orgf6ae25d">
1675 
 <p>
 1675 
 <p>
1676 
 <a id="ERT"></a><a href="./emdm_emwm_refl_ni.html#ERT"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
 1676 
 <a id="ERT"></a><a href="./emdm_emwm_refl_ni.html#ERT"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
1677 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
 1677 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
1678 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 1678 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
1679 
 </svg></a>
 1679 
 </svg></a>
1680 
 </p>
 1680 
 </p>
1681 
-<div class="alteqlabels" id="orgca80cb9">
1681 
+<div class="alteqlabels" id="org17eb76a">
1682 
 <ul class="org-ul">
 1682 
 <ul class="org-ul">
1683 
 <li>Gr (9.82)</li>
 1683 
 <li>Gr (9.82)</li>
1684 
 </ul>
 1684 
 </ul>
1744 
 </div>
 1744 
 </div>
1745 
 <div id="postamble" class="status">
 1745 
 <div id="postamble" class="status">
1746 
 <p class="author">Author: Jean-Sébastien Caux</p>
 1746 
 <p class="author">Author: Jean-Sébastien Caux</p>
1747 
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
1747 
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
1748 
 <p class="validation"></p>
 1748 
 <p class="validation"></p>
1749 
 </div>
 1749 
 </div>
1750
1750

+ 15
- 15
build/emdm_emwm_refl_oi.html View File

1 
 <!DOCTYPE html>
 1 
 <!DOCTYPE html>
2 
 <html lang="en">
 2 
 <html lang="en">
3 
 <head>
 3 
 <head>
4 
-<!-- 2022-03-22 Tue 10:52 -->
4 
+<!-- 2022-03-24 Thu 08:42 -->
5 
 <meta charset="utf-8">
 5 
 <meta charset="utf-8">
6 
 <meta name="viewport" content="width=device-width, initial-scale=1">
 6 
 <meta name="viewport" content="width=device-width, initial-scale=1">
7 
 <title>Pre-Quantum Electrodynamics</title>
 7 
 <title>Pre-Quantum Electrodynamics</title>
1293 
 </summary>
 1293 
 </summary>
1294 
 <ul>
 1294 
 <ul>
1295 
 <li>
 1295 
 <li>
1296 
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
1296 
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
1297
1297
1298 
 </li>
 1298 
 </li>
1299
1299
1635 
 \]
 1635 
 \]
1636 
 All waves have the same frequency \(\omega\). Since \(\omega = k v\), the three wavevectors are related by
 1636 
 All waves have the same frequency \(\omega\). Since \(\omega = k v\), the three wavevectors are related by
1637 
 </p>
 1637 
 </p>
1638 
-<div class="eqlabel" id="orgd898837">
1638 
+<div class="eqlabel" id="org512368e">
1639 
 <p>
 1639 
 <p>
1640 
 <a id="RTobliquek"></a><a href="./emdm_emwm_refl_oi.html#RTobliquek"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
 1640 
 <a id="RTobliquek"></a><a href="./emdm_emwm_refl_oi.html#RTobliquek"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
1641 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
 1641 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
1642 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 1642 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
1643 
 </svg></a>
 1643 
 </svg></a>
1644 
 </p>
 1644 
 </p>
1645 
-<div class="alteqlabels" id="orgabe9175">
1645 
+<div class="alteqlabels" id="org1361b67">
1646
1646
1647 
 </div>
 1647 
 </div>
1648
1648
1665 
 <p>
 1665 
 <p>
1666 
 From now on we will orient the axes so that \({\boldsymbol k}_I\) lies in the \(xz\) plane. This means that \({\boldsymbol k}_R\) and \({\boldsymbol k}_T\) also lie in that plane. This is the
 1666 
 From now on we will orient the axes so that \({\boldsymbol k}_I\) lies in the \(xz\) plane. This means that \({\boldsymbol k}_R\) and \({\boldsymbol k}_T\) also lie in that plane. This is the
1667 
 </p>
 1667 
 </p>
1668 
-<div class="core div" id="org4e7e42a">
1668 
+<div class="core div" id="org86dbe79">
1669 
 <p>
 1669 
 <p>
1670 
 <b>First law of reflection:</b>
 1670 
 <b>First law of reflection:</b>
1671 
   the incident, reflected and transmitted wave vectors form a plane (called the plane of incidence) which also includes the normal to the surface.
 1671 
   the incident, reflected and transmitted wave vectors form a plane (called the plane of incidence) which also includes the normal to the surface.
1680 
 with the incidence (\(\theta_I\)) and reflection (\(\theta_R\)) angles
 1680 
 with the incidence (\(\theta_I\)) and reflection (\(\theta_R\)) angles
1681 
 and the angle of refraction (\(\theta_T\)) obey the following laws:
 1681 
 and the angle of refraction (\(\theta_T\)) obey the following laws:
1682 
 </p>
 1682 
 </p>
1683 
-<div class="core div" id="org99d6843">
1683 
+<div class="core div" id="orge55fc76">
1684 
 <p>
 1684 
 <p>
1685 
 <b>Law of reflection</b>
 1685 
 <b>Law of reflection</b>
1686 
   \[
 1686 
   \[
1697 
 <p>
 1697 
 <p>
1698 
 This takes care of the spatially-dependent exponential factors in the boundary conditions. The coefficients must further obey
 1698 
 This takes care of the spatially-dependent exponential factors in the boundary conditions. The coefficients must further obey
1699 
 </p>
 1699 
 </p>
1700 
-<div class="eqlabel" id="orgdc0e7b2">
1700 
+<div class="eqlabel" id="orga2e8f02">
1701 
 <p>
 1701 
 <p>
1702 
 <a id="EBRT"></a><a href="./emdm_emwm_refl_oi.html#EBRT"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
 1702 
 <a id="EBRT"></a><a href="./emdm_emwm_refl_oi.html#EBRT"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
1703 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
 1703 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
1704 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 1704 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
1705 
 </svg></a>
 1705 
 </svg></a>
1706 
 </p>
 1706 
 </p>
1707 
-<div class="alteqlabels" id="org6d39cd4">
1707 
+<div class="alteqlabels" id="org12decff">
1708
1708
1709 
 </div>
 1709 
 </div>
1710
1710
1750 
 \]
 1750 
 \]
1751 
 Writing everything in terms of the incident amplitude, we get
 1751 
 Writing everything in terms of the incident amplitude, we get
1752 
 </p>
 1752 
 </p>
1753 
-<div class="main div" id="org1929cd0">
1753 
+<div class="main div" id="org29006a2">
1754 
 <p>
 1754 
 <p>
1755 
 <b>Fresnel's equations for reflection and transmission amplitudes (parallel case)</b>
 1755 
 <b>Fresnel's equations for reflection and transmission amplitudes (parallel case)</b>
1756 
 </p>
 1756 
 </p>
1757 
-<div class="eqlabel" id="org0b8be69">
1757 
+<div class="eqlabel" id="orgd431e6b">
1758 
 <p>
 1758 
 <p>
1759 
 <a id="Fresnel"></a><a href="./emdm_emwm_refl_oi.html#Fresnel"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
 1759 
 <a id="Fresnel"></a><a href="./emdm_emwm_refl_oi.html#Fresnel"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
1760 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
 1760 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
1761 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 1761 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
1762 
 </svg></a>
 1762 
 </svg></a>
1763 
 </p>
 1763 
 </p>
1764 
-<div class="alteqlabels" id="org617a8e4">
1764 
+<div class="alteqlabels" id="orgd3db507">
1765
1765
1766 
 </div>
 1766 
 </div>
1767
1767
1785 
 Behaviour: for \(\theta_I = 0\) we recover <a href="./emdm_emwm_refl_ni.html#ERT">ERT</a>.
 1785 
 Behaviour: for \(\theta_I = 0\) we recover <a href="./emdm_emwm_refl_ni.html#ERT">ERT</a>.
1786 
 For grazing waves \(\theta_I \rightarrow \pi/2\) we have that \(\alpha \rightarrow \infty\) and the wave is totally reflected. The most interesting angle is the one at which \(\alpha = \beta\) and the reflected wave has zero amplitude. This is known as
 1786 
 For grazing waves \(\theta_I \rightarrow \pi/2\) we have that \(\alpha \rightarrow \infty\) and the wave is totally reflected. The most interesting angle is the one at which \(\alpha = \beta\) and the reflected wave has zero amplitude. This is known as
1787 
 </p>
 1787 
 </p>
1788 
-<div class="main div" id="org087c316">
1789 
-<div class="eqlabel" id="orgb61a423">
1788 
+<div class="main div" id="orgff8c46e">
1789 
+<div class="eqlabel" id="org7aac922">
1790 
 <p>
 1790 
 <p>
1791 
 <a id="Brewster"></a><a href="./emdm_emwm_refl_oi.html#Brewster"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
 1791 
 <a id="Brewster"></a><a href="./emdm_emwm_refl_oi.html#Brewster"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
1792 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
 1792 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
1793 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 1793 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
1794 
 </svg></a>
 1794 
 </svg></a>
1795 
 </p>
 1795 
 </p>
1796 
-<div class="alteqlabels" id="org4e4ad5e">
1796 
+<div class="alteqlabels" id="orgb13b73c">
1797
1797
1798 
 </div>
 1798 
 </div>
1799
1799
1846 
 </div>
 1846 
 </div>
1847 
 <div id="postamble" class="status">
 1847 
 <div id="postamble" class="status">
1848 
 <p class="author">Author: Jean-Sébastien Caux</p>
 1848 
 <p class="author">Author: Jean-Sébastien Caux</p>
1849 
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1636 
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1642 
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 <p class="author">Author: Jean-Sébastien Caux</p>
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1686 
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1696 
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 Objectives
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 <p class="author">Author: Jean-Sébastien Caux</p>
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 <p class="author">Author: Jean-Sébastien Caux</p>
1663 
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1660 
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1660 
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 <p class="author">Author: Jean-Sébastien Caux</p>
1659 
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1659 
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1295 
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-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
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 1616 
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1617 
 A more aesthetic choice is the <b>Lorenz gauge</b>:
 1617 
 A more aesthetic choice is the <b>Lorenz gauge</b>:
1618 
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1619 
-<div class="eqlabel" id="orgb29b121">
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+<div class="eqlabel" id="org3de3f9b">
1620 
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 <p>
1621 
 <a id="LorenzG"></a><a href="./emf_g_Lg.html#LorenzG"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
 1621 
 <a id="LorenzG"></a><a href="./emf_g_Lg.html#LorenzG"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
1622 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
 1622 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
1623 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 1623 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
1624 
 </svg></a>
 1624 
 </svg></a>
1625 
 </p>
 1625 
 </p>
1626 
-<div class="alteqlabels" id="org2006eb5">
1626 
+<div class="alteqlabels" id="orgc9fe8ca">
1627
1627
1628 
 </div>
 1628 
 </div>
1629
1629
1635 
 \]
 1635 
 \]
1636 
 which is chosen to put the second term in the left-hand side of <a href="./emf_svp.html#LapA">LapA</a> to zero. What remains is then
 1636 
 which is chosen to put the second term in the left-hand side of <a href="./emf_svp.html#LapA">LapA</a> to zero. What remains is then
1637 
 </p>
 1637 
 </p>
1638 
-<div class="eqlabel" id="orgcba4a5d">
1638 
+<div class="eqlabel" id="org5b3094e">
1639 
 <p>
 1639 
 <p>
1640 
 <a id="ALorenzG"></a><a href="./emf_g_Lg.html#ALorenzG"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
 1640 
 <a id="ALorenzG"></a><a href="./emf_g_Lg.html#ALorenzG"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
1641 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
 1641 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
1642 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 1642 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
1643 
 </svg></a>
 1643 
 </svg></a>
1644 
 </p>
 1644 
 </p>
1645 
-<div class="alteqlabels" id="org2d4cecb">
1645 
+<div class="alteqlabels" id="org687131e">
1646
1646
1647 
 </div>
 1647 
 </div>
1648
1648
1654 
 \]
 1654 
 \]
1655 
 while the equation for \(\phi\) becomes
 1655 
 while the equation for \(\phi\) becomes
1656 
 </p>
 1656 
 </p>
1657 
-<div class="eqlabel" id="org7c6aebc">
1657 
+<div class="eqlabel" id="org29d69e0">
1658 
 <p>
 1658 
 <p>
1659 
 <a id="phiLorenzG"></a><a href="./emf_g_Lg.html#phiLorenzG"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
 1659 
 <a id="phiLorenzG"></a><a href="./emf_g_Lg.html#phiLorenzG"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
1660 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
 1660 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
1661 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 1661 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
1662 
 </svg></a>
 1662 
 </svg></a>
1663 
 </p>
 1663 
 </p>
1664 
-<div class="alteqlabels" id="org8b3cda4">
1664 
+<div class="alteqlabels" id="org4856773">
1665
1665
1666 
 </div>
 1666 
 </div>
1667
1667
1673 
 \]
 1673 
 \]
1674 
 These can be written compactly upon introducing a new operator: the
 1674 
 These can be written compactly upon introducing a new operator: the
1675 
 </p>
 1675 
 </p>
1676 
-<div class="core div" id="orgd056ba8">
1676 
+<div class="core div" id="orga269826">
1677 
 <p>
 1677 
 <p>
1678 
 <b>d'Alembertian operator</b>
 1678 
 <b>d'Alembertian operator</b>
1679 
 </p>
 1679 
 </p>
1680 
-<div class="eqlabel" id="orgfd937d0">
1680 
+<div class="eqlabel" id="org39fa795">
1681 
 <p>
 1681 
 <p>
1682 
 <a id="dAl"></a><a href="./emf_g_Lg.html#dAl"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
 1682 
 <a id="dAl"></a><a href="./emf_g_Lg.html#dAl"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
1683 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
 1683 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
1684 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 1684 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
1685 
 </svg></a>
 1685 
 </svg></a>
1686 
 </p>
 1686 
 </p>
1687 
-<div class="alteqlabels" id="org57101d6">
1687 
+<div class="alteqlabels" id="orgf4aa848">
1688
1688
1689 
 </div>
 1689 
 </div>
1690
1690
1700 
 <p>
 1700 
 <p>
1701 
 so we get the
 1701 
 so we get the
1702 
 </p>
 1702 
 </p>
1703 
-<div class="core div" id="org037b830">
1703 
+<div class="core div" id="org65e01f8">
1704 
 <p>
 1704 
 <p>
1705 
 <b>Inhomogeneous Maxwell equations</b> <i>(Lorenz gauge)</i>
 1705 
 <b>Inhomogeneous Maxwell equations</b> <i>(Lorenz gauge)</i>
1706 
 </p>
 1706 
 </p>
1707 
-<div class="eqlabel" id="org9dce32f">
1707 
+<div class="eqlabel" id="orgc262f70">
1708 
 <p>
 1708 
 <p>
1709 
 <a id="MaxLor"></a><a href="./emf_g_Lg.html#MaxLor"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
 1709 
 <a id="MaxLor"></a><a href="./emf_g_Lg.html#MaxLor"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
1710 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
 1710 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
1711 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 1711 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
1712 
 </svg></a>
 1712 
 </svg></a>
1713 
 </p>
 1713 
 </p>
1714 
-<div class="alteqlabels" id="org22f6c85">
1714 
+<div class="alteqlabels" id="orgc540066">
1715
1715
1716 
 </div>
 1716 
 </div>
1717
1717
1764 
 </div>
 1764 
 </div>
1765 
 <div id="postamble" class="status">
 1765 
 <div id="postamble" class="status">
1766 
 <p class="author">Author: Jean-Sébastien Caux</p>
 1766 
 <p class="author">Author: Jean-Sébastien Caux</p>
1767 
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
1767 
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
1768 
 <p class="validation"></p>
 1768 
 <p class="validation"></p>
1769 
 </div>
 1769 
 </div>
1770
1770

+ 13
- 13
build/emf_svp.html View File

1 
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2 
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 <html lang="en">
3 
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 <head>
4 
-<!-- 2022-03-22 Tue 10:52 -->
4 
+<!-- 2022-03-24 Thu 08:42 -->
5 
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 5 
 <meta charset="utf-8">
6 
 <meta name="viewport" content="width=device-width, initial-scale=1">
 6 
 <meta name="viewport" content="width=device-width, initial-scale=1">
7 
 <title>Pre-Quantum Electrodynamics</title>
 7 
 <title>Pre-Quantum Electrodynamics</title>
1293 
 </summary>
 1293 
 </summary>
1294 
 <ul>
 1294 
 <ul>
1295 
 <li>
 1295 
 <li>
1296 
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
1296 
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
1297
1297
1298 
 </li>
 1298 
 </li>
1299
1299
1631 
 Easiest: as we already saw (<a href="./ems_ms_vp_A.html#BcurlA">BcurlA</a>), we can write the magnetic
 1631 
 Easiest: as we already saw (<a href="./ems_ms_vp_A.html#BcurlA">BcurlA</a>), we can write the magnetic
1632 
 field as a pure curl (since its divergence always vanishes):
 1632 
 field as a pure curl (since its divergence always vanishes):
1633 
 </p>
 1633 
 </p>
1634 
-<div class="core div" id="org0868f0a">
1634 
+<div class="core div" id="org913ae4e">
1635 
 <p>
 1635 
 <p>
1636 
 \[
 1636 
 \[
1637 
 {\boldsymbol B} = {\boldsymbol \nabla} \times {\boldsymbol A}
 1637 
 {\boldsymbol B} = {\boldsymbol \nabla} \times {\boldsymbol A}
1648 
 so this can be written as the gradient of a scalar.
 1648 
 so this can be written as the gradient of a scalar.
1649 
 Making the choice \(-{\boldsymbol \nabla} \phi\) for this, we get
 1649 
 Making the choice \(-{\boldsymbol \nabla} \phi\) for this, we get
1650 
 </p>
 1650 
 </p>
1651 
-<div class="core div" id="org5ea4990">
1652 
-<div class="eqlabel" id="orgccc2c0e">
1651 
+<div class="core div" id="orgcc3047e">
1652 
+<div class="eqlabel" id="org50da26e">
1653 
 <p>
 1653 
 <p>
1654 
 <a id="E_phiA"></a><a href="./emf_svp.html#E_phiA"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
 1654 
 <a id="E_phiA"></a><a href="./emf_svp.html#E_phiA"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
1655 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
 1655 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
1656 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 1656 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
1657 
 </svg></a>
 1657 
 </svg></a>
1658 
 </p>
 1658 
 </p>
1659 
-<div class="alteqlabels" id="orgc2e0dbe">
1659 
+<div class="alteqlabels" id="org3a04a5a">
1660
1660
1661 
 </div>
 1661 
 </div>
1662
1662
1673 
 <p>
 1673 
 <p>
1674 
 Using this potential representation for \({\boldsymbol E}\) and \({\boldsymbol B}\) automatically fulfills the two homogeneous Maxwell equations. For the inhomogeneous equations, substituting <a href="./emf_svp.html#E_phiA">E_phiA</a> into Gauss's law gives
 1674 
 Using this potential representation for \({\boldsymbol E}\) and \({\boldsymbol B}\) automatically fulfills the two homogeneous Maxwell equations. For the inhomogeneous equations, substituting <a href="./emf_svp.html#E_phiA">E_phiA</a> into Gauss's law gives
1675 
 </p>
 1675 
 </p>
1676 
-<div class="main div" id="org7ca77db">
1677 
-<div class="eqlabel" id="org49309f0">
1676 
+<div class="main div" id="orge407b00">
1677 
+<div class="eqlabel" id="orgad33676">
1678 
 <p>
 1678 
 <p>
1679 
 <a id="Lapphi"></a><a href="./emf_svp.html#Lapphi"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
 1679 
 <a id="Lapphi"></a><a href="./emf_svp.html#Lapphi"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
1680 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
 1680 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
1681 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 1681 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
1682 
 </svg></a>
 1682 
 </svg></a>
1683 
 </p>
 1683 
 </p>
1684 
-<div class="alteqlabels" id="org1b03eff">
1684 
+<div class="alteqlabels" id="org4f2824a">
1685
1685
1686 
 </div>
 1686 
 </div>
1687
1687
1701 
 \]
 1701 
 \]
1702 
 which becomes after simple rearrangement and use of the <a href="./c_m_dc_d2.html#curlcurl">curlcurl</a> identity \({\boldsymbol \nabla} \times \left({\boldsymbol \nabla} \times {\boldsymbol A}\right) = {\boldsymbol \nabla} ({\boldsymbol \nabla} \cdot {\boldsymbol A}) - {\boldsymbol \nabla}^2 {\boldsymbol A}\),
 1702 
 which becomes after simple rearrangement and use of the <a href="./c_m_dc_d2.html#curlcurl">curlcurl</a> identity \({\boldsymbol \nabla} \times \left({\boldsymbol \nabla} \times {\boldsymbol A}\right) = {\boldsymbol \nabla} ({\boldsymbol \nabla} \cdot {\boldsymbol A}) - {\boldsymbol \nabla}^2 {\boldsymbol A}\),
1703 
 </p>
 1703 
 </p>
1704 
-<div class="main div" id="org930bf11">
1705 
-<div class="eqlabel" id="org7818374">
1704 
+<div class="main div" id="orga4d93c1">
1705 
+<div class="eqlabel" id="orgbbedeec">
1706 
 <p>
 1706 
 <p>
1707 
 <a id="LapA"></a><a href="./emf_svp.html#LapA"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
 1707 
 <a id="LapA"></a><a href="./emf_svp.html#LapA"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
1708 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
 1708 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
1709 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 1709 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
1710 
 </svg></a>
 1710 
 </svg></a>
1711 
 </p>
 1711 
 </p>
1712 
-<div class="alteqlabels" id="org9e9918d">
1712 
+<div class="alteqlabels" id="orgb9a7aee">
1713
1713
1714 
 </div>
 1714 
 </div>
1715
1715
1744 
 </div>
 1744 
 </div>
1745 
 <div id="postamble" class="status">
 1745 
 <div id="postamble" class="status">
1746 
 <p class="author">Author: Jean-Sébastien Caux</p>
 1746 
 <p class="author">Author: Jean-Sébastien Caux</p>
1747 
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
1747 
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
1748 
 <p class="validation"></p>
 1748 
 <p class="validation"></p>
1749 
 </div>
 1749 
 </div>
1750
1750

+ 3
- 3
build/ems.html View File

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2 
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3 
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 <meta name="viewport" content="width=device-width, initial-scale=1">
7 
 <title>Pre-Quantum Electrodynamics</title>
 7 
 <title>Pre-Quantum Electrodynamics</title>
1293 
 </summary>
 1293 
 </summary>
1294 
 <ul>
 1294 
 <ul>
1295 
 <li>
 1295 
 <li>
1296 
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
1296 
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
1297
1297
1298 
 </li>
 1298 
 </li>
1299
1299
1640 
 </div>
 1640 
 </div>
1641 
 <div id="postamble" class="status">
 1641 
 <div id="postamble" class="status">
1642 
 <p class="author">Author: Jean-Sébastien Caux</p>
 1642 
 <p class="author">Author: Jean-Sébastien Caux</p>
1643 
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
1643 
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
1644 
 <p class="validation"></p>
 1644 
 <p class="validation"></p>
1645 
 </div>
 1645 
 </div>
1646
1646

+ 7
- 7
build/ems_ca.html View File

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 <meta name="viewport" content="width=device-width, initial-scale=1">
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 <meta name="viewport" content="width=device-width, initial-scale=1">
7 
 <title>Pre-Quantum Electrodynamics</title>
 7 
 <title>Pre-Quantum Electrodynamics</title>
1293 
 </summary>
 1293 
 </summary>
1294 
 <ul>
 1294 
 <ul>
1295 
 <li>
 1295 
 <li>
1296 
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
1296 
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
1297
1297
1298 
 </li>
 1298 
 </li>
1299
1299
1618 
 <li>Gr 3</li>
 1618 
 <li>Gr 3</li>
1619 
 </ul>
 1619 
 </ul>
1620
1620
1621 
-<details class="prereq" id="orgd0e4e8d">
1622 
-<summary id="org949c0df">
1621 
+<details class="prereq" id="org587aea3">
1622 
+<summary id="orgf03fd4d">
1623 
 Prerequisites
 1623 
 Prerequisites
1624 
 </summary>
 1624 
 </summary>
1625 
 <ul class="org-ul">
 1625 
 <ul class="org-ul">
1627 
 </ul>
 1627 
 </ul>
1628 
 </details>
 1628 
 </details>
1629
1629
1630 
-<details class="objectives" id="orgfb8d074">
1631 
-<summary id="org39be3a5">
1630 
+<details class="objectives" id="orgedf1d47">
1631 
+<summary id="orgbfc64ab">
1632 
 Objectives
 1632 
 Objectives
1633 
 </summary>
 1633 
 </summary>
1634 
 <ul class="org-ul">
 1634 
 <ul class="org-ul">
1666 
 </div>
 1666 
 </div>
1667 
 <div id="postamble" class="status">
 1667 
 <div id="postamble" class="status">
1668 
 <p class="author">Author: Jean-Sébastien Caux</p>
 1668 
 <p class="author">Author: Jean-Sébastien Caux</p>
1669 
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
1669 
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
1670 
 <p class="validation"></p>
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 <p class="validation"></p>
1671 
 </div>
 1671 
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1672
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build/ems_ca_fe.html View File

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3 
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7 
 <title>Pre-Quantum Electrodynamics</title>
 7 
 <title>Pre-Quantum Electrodynamics</title>
1293 
 </summary>
 1293 
 </summary>
1294 
 <ul>
 1294 
 <ul>
1295 
 <li>
 1295 
 <li>
1296 
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
1296 
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
1297
1297
1298 
 </li>
 1298 
 </li>
1299
1299
1624 
 defines an electrostatic problem, whose solution is in principle obtained
 1624 
 defines an electrostatic problem, whose solution is in principle obtained
1625 
 from calculating either the field according to <a href="./ems_es_ef_ccd.html#E_vcd">E_vcd</a>
 1625 
 from calculating either the field according to <a href="./ems_es_ef_ccd.html#E_vcd">E_vcd</a>
1626 
 </p>
 1626 
 </p>
1627 
-<div class="main div" id="org8236a16">
1627 
+<div class="main div" id="orgce1c4bf">
1628 
 <p>
 1628 
 <p>
1629
1629
1630 
 </p>
 1630 
 </p>
1638 
 or (often simpler) by calculating the electrostatic potential, using either the
 1638 
 or (often simpler) by calculating the electrostatic potential, using either the
1639 
 explicit construction <a href="./ems_es_ep_d.html#p_vcd">p_vcd</a>
 1639 
 explicit construction <a href="./ems_es_ep_d.html#p_vcd">p_vcd</a>
1640 
 </p>
 1640 
 </p>
1641 
-<div class="main div" id="orgd333b49">
1641 
+<div class="main div" id="orge8cb758">
1642 
 <p>
 1642 
 <p>
1643
1643
1644 
 </p>
 1644 
 </p>
1658 
 <a href="./ems_es_ep_PL.html#Poi">🐟</a>
 1658 
 <a href="./ems_es_ep_PL.html#Poi">🐟</a>
1659 
 </p>
 1659 
 </p>
1660
1660
1661 
-<div class="core div" id="orge399a4f">
1661 
+<div class="core div" id="org65cda5b">
1662 
 <p>
 1662 
 <p>
1663
1663
1664 
 </p>
 1664 
 </p>
1674 
 <p>
 1674 
 <p>
1675 
 In the specific case where the charge density vanishes, we fall back onto the simpler Laplace equation <a href="./ems_es_ep_PL.html#Lap">Lap</a>
 1675 
 In the specific case where the charge density vanishes, we fall back onto the simpler Laplace equation <a href="./ems_es_ep_PL.html#Lap">Lap</a>
1676 
 </p>
 1676 
 </p>
1677 
-<div class="core div" id="orgea54c28">
1677 
+<div class="core div" id="org9318a15">
1678 
 <p>
 1678 
 <p>
1679
1679
1680 
 </p>
 1680 
 </p>
1712 
 </div>
 1712 
 </div>
1713 
 <div id="postamble" class="status">
 1713 
 <div id="postamble" class="status">
1714 
 <p class="author">Author: Jean-Sébastien Caux</p>
 1714 
 <p class="author">Author: Jean-Sébastien Caux</p>
1715 
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
1715 
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
1716 
 <p class="validation"></p>
 1716 
 <p class="validation"></p>
1717 
 </div>
 1717 
 </div>
1718
1718

+ 20
- 20
build/ems_ca_fe_L.html View File

1 
 <!DOCTYPE html>
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 <!DOCTYPE html>
2 
 <html lang="en">
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 <html lang="en">
3 
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 <head>
4 
-<!-- 2022-03-22 Tue 10:52 -->
4 
+<!-- 2022-03-24 Thu 08:42 -->
5 
 <meta charset="utf-8">
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 <meta charset="utf-8">
6 
 <meta name="viewport" content="width=device-width, initial-scale=1">
 6 
 <meta name="viewport" content="width=device-width, initial-scale=1">
7 
 <title>Pre-Quantum Electrodynamics</title>
 7 
 <title>Pre-Quantum Electrodynamics</title>
1293 
 </summary>
 1293 
 </summary>
1294 
 <ul>
 1294 
 <ul>
1295 
 <li>
 1295 
 <li>
1296 
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
1296 
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
1297
1297
1298 
 </li>
 1298 
 </li>
1299
1299
1630 
 function \(\phi (x)\) and the Laplace equation reads
 1630 
 function \(\phi (x)\) and the Laplace equation reads
1631 
 </p>
 1631 
 </p>
1632
1632
1633 
-<div class="eqlabel" id="orgd14f5e0">
1633 
+<div class="eqlabel" id="orgd38ad90">
1634 
 <p>
 1634 
 <p>
1635 
 <a id="Lap_1d"></a><a href="./ems_ca_fe_L.html#Lap_1d"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
 1635 
 <a id="Lap_1d"></a><a href="./ems_ca_fe_L.html#Lap_1d"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
1636 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
 1636 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
1637 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 1637 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
1638 
 </svg></a>
 1638 
 </svg></a>
1639 
 </p>
 1639 
 </p>
1640 
-<div class="alteqlabels" id="orgdd168eb">
1640 
+<div class="alteqlabels" id="org23686dc">
1641
1641
1642 
 </div>
 1642 
 </div>
1643
1643
1652 
 <p>
 1652 
 <p>
1653 
 The solution to this is
 1653 
 The solution to this is
1654 
 </p>
 1654 
 </p>
1655 
-<div class="eqlabel" id="org9e3195b">
1655 
+<div class="eqlabel" id="org78665cb">
1656 
 <p>
 1656 
 <p>
1657 
 <a id="Lap_1d_sol"></a><a href="./ems_ca_fe_L.html#Lap_1d_sol"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
 1657 
 <a id="Lap_1d_sol"></a><a href="./ems_ca_fe_L.html#Lap_1d_sol"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
1658 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
 1658 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
1659 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 1659 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
1660 
 </svg></a>
 1660 
 </svg></a>
1661 
 </p>
 1661 
 </p>
1662 
-<div class="alteqlabels" id="org7a39d73">
1662 
+<div class="alteqlabels" id="orge0dbdb5">
1663 
 <ul class="org-ul">
 1663 
 <ul class="org-ul">
1664 
 <li>Gr (3.6)</li>
 1664 
 <li>Gr (3.6)</li>
1665 
 </ul>
 1665 
 </ul>
1718 
 of two variables (here: \(x\) and \(y\)), so Laplace's
 1718 
 of two variables (here: \(x\) and \(y\)), so Laplace's
1719 
 equation now reads
 1719 
 equation now reads
1720 
 </p>
 1720 
 </p>
1721 
-<div class="eqlabel" id="org01996f8">
1721 
+<div class="eqlabel" id="orgd4e7f28">
1722 
 <p>
 1722 
 <p>
1723 
 <a id="Lap_2d"></a><a href="./ems_ca_fe_L.html#Lap_2d"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
 1723 
 <a id="Lap_2d"></a><a href="./ems_ca_fe_L.html#Lap_2d"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
1724 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
 1724 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
1725 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 1725 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
1726 
 </svg></a>
 1726 
 </svg></a>
1727 
 </p>
 1727 
 </p>
1728 
-<div class="alteqlabels" id="org518eefc">
1728 
+<div class="alteqlabels" id="orga64f9ad">
1729
1729
1730 
 </div>
 1730 
 </div>
1731
1731
1778 
 \(S_R({\bf r})\) of any radius \(R\) centered on this point
 1778 
 \(S_R({\bf r})\) of any radius \(R\) centered on this point
1779 
 (and of course not containing any charges),
 1779 
 (and of course not containing any charges),
1780 
 </p>
 1780 
 </p>
1781 
-<div class="eqlabel" id="org1ec3447">
1781 
+<div class="eqlabel" id="org598b2e6">
1782 
 <p>
 1782 
 <p>
1783 
 <a id="p_ball_avg"></a><a href="./ems_ca_fe_L.html#p_ball_avg"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
 1783 
 <a id="p_ball_avg"></a><a href="./ems_ca_fe_L.html#p_ball_avg"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
1784 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
 1784 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
1785 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 1785 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
1786 
 </svg></a>
 1786 
 </svg></a>
1787 
 </p>
 1787 
 </p>
1788 
-<div class="alteqlabels" id="org832c6a2">
1788 
+<div class="alteqlabels" id="orgdb48832">
1789
1789
1790 
 </div>
 1790 
 </div>
1791
1791
1797 
 \]
 1797 
 \]
1798 
 </p>
 1798 
 </p>
1799
1799
1800 
-<details id="org653c3ca">
1801 
-<summary id="org9063816">
1800 
+<details id="orgd997cbe">
1801 
+<summary id="org6b22e3f">
1802 
 <strong>Physicist's proof</strong>
 1802 
 <strong>Physicist's proof</strong>
1803 
 </summary>
 1803 
 </summary>
1804 
 <p>
 1804 
 <p>
1860 
 </p>
 1860 
 </p>
1861 
 </details>
 1861 
 </details>
1862
1862
1863 
-<details id="org086b4a6">
1864 
-<summary id="orgd2d3c6e">
1863 
+<details id="org2ff5eec">
1864 
+<summary id="orgc0446a1">
1865 
 <strong>Formal proof</strong>
 1865 
 <strong>Formal proof</strong>
1866 
 </summary>
 1866 
 </summary>
1867
1867
1911 
 <p>
 1911 
 <p>
1912 
 <b>Theorem</b>:
 1912 
 <b>Theorem</b>:
1913 
 </p>
 1913 
 </p>
1914 
-<div class="eqlabel" id="org6d0244a">
1914 
+<div class="eqlabel" id="orge37257a">
1915 
 <p>
 1915 
 <p>
1916 
 <a id="dfdR_intLap"></a><a href="./ems_ca_fe_L.html#dfdR_intLap"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
 1916 
 <a id="dfdR_intLap"></a><a href="./ems_ca_fe_L.html#dfdR_intLap"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
1917 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
 1917 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
1918 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 1918 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
1919 
 </svg></a>
 1919 
 </svg></a>
1920 
 </p>
 1920 
 </p>
1921 
-<div class="alteqlabels" id="org227c883">
1921 
+<div class="alteqlabels" id="orgb3a7f07">
1922
1922
1923 
 </div>
 1923 
 </div>
1924
1924
1971 
 of the \(f_x + f_y + f_z = 0\) condition above.
 1971 
 of the \(f_x + f_y + f_z = 0\) condition above.
1972 
 </p>
 1972 
 </p>
1973
1973
1974 
-<div class="eqlabel" id="orga00aa93">
1974 
+<div class="eqlabel" id="org39eb572">
1975 
 <p>
 1975 
 <p>
1976 
 <a id="Earnshaw"></a><a href="./ems_ca_fe_L.html#Earnshaw"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
 1976 
 <a id="Earnshaw"></a><a href="./ems_ca_fe_L.html#Earnshaw"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
1977 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
 1977 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
1978 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 1978 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
1979 
 </svg></a>
 1979 
 </svg></a>
1980 
 </p>
 1980 
 </p>
1981 
-<div class="alteqlabels" id="orge0f050e">
1981 
+<div class="alteqlabels" id="org2cc4d11">
1982
1982
1983 
 </div>
 1983 
 </div>
1984
1984
1985 
 </div>
 1985 
 </div>
1986 
-<div class="info div" id="org81fcf04">
1986 
+<div class="info div" id="orgcd59178">
1987 
 <p>
 1987 
 <p>
1988 
 <b>Earnshaw's theorem (physical version)</b> <br>
 1988 
 <b>Earnshaw's theorem (physical version)</b> <br>
1989 
 </p>
 1989 
 </p>
2102 
 </div>
 2102 
 </div>
2103 
 <div id="postamble" class="status">
 2103 
 <div id="postamble" class="status">
2104 
 <p class="author">Author: Jean-Sébastien Caux</p>
 2104 
 <p class="author">Author: Jean-Sébastien Caux</p>
2105 
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
2105 
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
2106 
 <p class="validation"></p>
 2106 
 <p class="validation"></p>
2107 
 </div>
 2107 
 </div>
2108
2108

+ 9
- 9
build/ems_ca_fe_g.html View File

1 
 <!DOCTYPE html>
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 <!DOCTYPE html>
2 
 <html lang="en">
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 <html lang="en">
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 <head>
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 <head>
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-<!-- 2022-03-22 Tue 10:52 -->
4 
+<!-- 2022-03-24 Thu 08:42 -->
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 <meta charset="utf-8">
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 <meta charset="utf-8">
6 
 <meta name="viewport" content="width=device-width, initial-scale=1">
 6 
 <meta name="viewport" content="width=device-width, initial-scale=1">
7 
 <title>Pre-Quantum Electrodynamics</title>
 7 
 <title>Pre-Quantum Electrodynamics</title>
1293 
 </summary>
 1293 
 </summary>
1294 
 <ul>
 1294 
 <ul>
1295 
 <li>
 1295 
 <li>
1296 
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
1296 
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
1297
1297
1298 
 </li>
 1298 
 </li>
1299
1299
1613 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 1613 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
1614 
 </svg></a><span class="headline-id">ems.ca.fe.g</span></h5>
 1614 
 </svg></a><span class="headline-id">ems.ca.fe.g</span></h5>
1615 
 <div class="outline-text-5" id="text-ems_ca_fe_g">
 1615 
 <div class="outline-text-5" id="text-ems_ca_fe_g">
1616 
-<div class="info div" id="orgef35f51">
1616 
+<div class="info div" id="org60c1b11">
1617 
 <p>
 1617 
 <p>
1618 
 <b>George Green</b>
 1618 
 <b>George Green</b>
1619 
 </p>
 1619 
 </p>
1620 
-<aside id="org432d494">
1620 
+<aside id="org0b1da41">
1621 
 <p>
 1621 
 <p>
1622 
 See a <a href="https://en.wikipedia.org/wiki/George%5C_Green%5C_(mathematician)">short bio on wikipedia</a>
 1622 
 See a <a href="https://en.wikipedia.org/wiki/George%5C_Green%5C_(mathematician)">short bio on wikipedia</a>
1623 
 </p>
 1623 
 </p>
1650 
 \]
 1650 
 \]
1651 
 Substituting this in the divergence theorem gives <b>Green's first identity</b>
 1651 
 Substituting this in the divergence theorem gives <b>Green's first identity</b>
1652 
 </p>
 1652 
 </p>
1653 
-<div class="eqlabel" id="orgfd30f5d">
1653 
+<div class="eqlabel" id="org3d01833">
1654 
 <p>
 1654 
 <p>
1655 
 <a id="Green1"></a><a href="./ems_ca_fe_g.html#Green1"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
 1655 
 <a id="Green1"></a><a href="./ems_ca_fe_g.html#Green1"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
1656 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
 1656 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
1657 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 1657 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
1658 
 </svg></a>
 1658 
 </svg></a>
1659 
 </p>
 1659 
 </p>
1660 
-<div class="alteqlabels" id="org3125160">
1660 
+<div class="alteqlabels" id="orga726fcd">
1661 
 <ul class="org-ul">
 1661 
 <ul class="org-ul">
1662 
 <li>J (1.34)</li>
 1662 
 <li>J (1.34)</li>
1663 
 </ul>
 1663 
 </ul>
1675 
 interchanged, and subtract the result, we obtain another useful result known as
 1675 
 interchanged, and subtract the result, we obtain another useful result known as
1676 
 <b>Green's second identity</b> or <b>Green's theorem</b>
 1676 
 <b>Green's second identity</b> or <b>Green's theorem</b>
1677 
 </p>
 1677 
 </p>
1678 
-<div class="eqlabel" id="org028fffd">
1678 
+<div class="eqlabel" id="org964d072">
1679 
 <p>
 1679 
 <p>
1680 
 <a id="Green2"></a><a href="./ems_ca_fe_g.html#Green2"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
 1680 
 <a id="Green2"></a><a href="./ems_ca_fe_g.html#Green2"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
1681 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
 1681 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
1682 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 1682 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
1683 
 </svg></a>
 1683 
 </svg></a>
1684 
 </p>
 1684 
 </p>
1685 
-<div class="alteqlabels" id="org9ea869b">
1685 
+<div class="alteqlabels" id="orge29c408">
1686 
 <ul class="org-ul">
 1686 
 <ul class="org-ul">
1687 
 <li>J (1.35)</li>
 1687 
 <li>J (1.35)</li>
1688 
 </ul>
 1688 
 </ul>
1718 
 </div>
 1718 
 </div>
1719 
 <div id="postamble" class="status">
 1719 
 <div id="postamble" class="status">
1720 
 <p class="author">Author: Jean-Sébastien Caux</p>
 1720 
 <p class="author">Author: Jean-Sébastien Caux</p>
1721 
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
1721 
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
1722 
 <p class="validation"></p>
 1722 
 <p class="validation"></p>
1723 
 </div>
 1723 
 </div>
1724
1724

+ 11
- 11
build/ems_ca_fe_uP.html View File

1 
 <!DOCTYPE html>
 1 
 <!DOCTYPE html>
2 
 <html lang="en">
 2 
 <html lang="en">
3 
 <head>
 3 
 <head>
4 
-<!-- 2022-03-22 Tue 10:52 -->
4 
+<!-- 2022-03-24 Thu 08:42 -->
5 
 <meta charset="utf-8">
 5 
 <meta charset="utf-8">
6 
 <meta name="viewport" content="width=device-width, initial-scale=1">
 6 
 <meta name="viewport" content="width=device-width, initial-scale=1">
7 
 <title>Pre-Quantum Electrodynamics</title>
 7 
 <title>Pre-Quantum Electrodynamics</title>
1293 
 </summary>
 1293 
 </summary>
1294 
 <ul>
 1294 
 <ul>
1295 
 <li>
 1295 
 <li>
1296 
-<a href="./qed_t.html#qed_t">QED today</a><span class="headline-id">qed.t</span>
1296 
+<a href="./qed_L.html#qed_L">Lagrangian</a><span class="headline-id">qed.L</span>
1297
1297
1298 
 </li>
 1298 
 </li>
1299
1299
1635 
 The first term on the left-hand side vanishes since \(\Phi\) satisfies Laplace.
 1635 
 The first term on the left-hand side vanishes since \(\Phi\) satisfies Laplace.
1636 
 The right-hand side can be made to vanish if \(\Phi\) obeys either
 1636 
 The right-hand side can be made to vanish if \(\Phi\) obeys either
1637 
 </p>
 1637 
 </p>
1638 
-<div class="eqlabel" id="orgfa460b1">
1638 
+<div class="eqlabel" id="org0acb722">
1639 
 <p>
 1639 
 <p>
1640 
 <a id="Dirichlet"></a><a href="./ems_ca_fe_uP.html#Dirichlet"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
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 <a id="Dirichlet"></a><a href="./ems_ca_fe_uP.html#Dirichlet"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
1641 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
 1641 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
1642 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 1642 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
1643 
 </svg></a>
 1643 
 </svg></a>
1644 
 </p>
 1644 
 </p>
1645 
-<div class="alteqlabels" id="org14f7efc">
1645 
+<div class="alteqlabels" id="org03f8c83">
1646
1646
1647 
 </div>
 1647 
 </div>
1648
1648
1654 
 <p>
 1654 
 <p>
1655 
 or
 1655 
 or
1656 
 </p>
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 </p>
1657 
-<div class="eqlabel" id="orgcd08c73">
1657 
+<div class="eqlabel" id="org3d1a359">
1658 
 <p>
 1658 
 <p>
1659 
 <a id="Neumann"></a><a href="./ems_ca_fe_uP.html#Neumann"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
 1659 
 <a id="Neumann"></a><a href="./ems_ca_fe_uP.html#Neumann"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
1660 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
 1660 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
1661 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 1661 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
1662 
 </svg></a>
 1662 
 </svg></a>
1663 
 </p>
 1663 
 </p>
1664 
-<div class="alteqlabels" id="org6976f14">
1664 
+<div class="alteqlabels" id="orga2c0bab">
1665
1665
1666 
 </div>
 1666 
 </div>
1667
1667
1689 
 <p>
 1689 
 <p>
1690 
 We can thus finally state the
 1690 
 We can thus finally state the
1691 
 </p>
 1691 
 </p>
1692 
-<div class="eqlabel" id="orgd45117f">
1692 
+<div class="eqlabel" id="orgf4dd440">
1693 
 <p>
 1693 
 <p>
1694 
 <a id="uniq_thm"></a><a href="./ems_ca_fe_uP.html#uniq_thm"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
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 <a id="uniq_thm"></a><a href="./ems_ca_fe_uP.html#uniq_thm"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
1695 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
 1695 
   <path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
1696 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
 1696 
   <path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
1697 
 </svg></a>
 1697 
 </svg></a>
1698 
 </p>
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 </p>
1699 
-<div class="alteqlabels" id="org2d283cb">
1699 
+<div class="alteqlabels" id="org786cfb7">
1700
1700
1701 
 </div>
 1701 
 </div>
1702
1702
1703 
 </div>
 1703 
 </div>
1704 
-<div class="core div" id="orgf2a5ea9">
1704 
+<div class="core div" id="org9b96393">
1705 
 <p>
 1705 
 <p>
1706 
 <b>Uniqueness Theorem</b>
 1706 
 <b>Uniqueness Theorem</b>
1707 
 </p>
 1707 
 </p>
1740 
 and corollaries and that things are
 1740 
 and corollaries and that things are
1741 
 </p>
 1741 
 </p>
1742
1742
1743 
-<div class="info div" id="orgd298dad">
1743 
+<div class="info div" id="org333667e">
1744 
 <p>
 1744 
 <p>
1745 
 <b>Comment/warning</b>: <b>uniqueness theorem on uniqueness theorems</b> <br>
 1745 
 <b>Comment/warning</b>: <b>uniqueness theorem on uniqueness theorems</b> <br>
1746 
   Do not be misled: there is a <i>unique</i> uniqueness theorem for the
 1746 
   Do not be misled: there is a <i>unique</i> uniqueness theorem for the
1767 
 </div>
 1767 
 </div>
1768 
 <div id="postamble" class="status">
 1768 
 <div id="postamble" class="status">
1769 
 <p class="author">Author: Jean-Sébastien Caux</p>
 1769 
 <p class="author">Author: Jean-Sébastien Caux</p>
1770 
-<p class="date">Created: 2022-03-22 Tue 10:52</p>
1770 
+<p class="date">Created: 2022-03-24 Thu 08:42</p>
1771 
 <p class="validation"></p>
 1771 
 <p class="validation"></p>
1772 
 </div>
 1772 
 </div>
1773
1773

+ 0
- 0
build/ems_ca_me.html View File


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