<?xml version="1.0" encoding="ISO-8859-1"?><article xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">
<front>
<journal-meta>
<journal-id>0035-001X</journal-id>
<journal-title><![CDATA[Revista mexicana de física]]></journal-title>
<abbrev-journal-title><![CDATA[Rev. mex. fis.]]></abbrev-journal-title>
<issn>0035-001X</issn>
<publisher>
<publisher-name><![CDATA[Sociedad Mexicana de Física]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S0035-001X2007001000004</article-id>
<title-group>
<article-title xml:lang="es"><![CDATA[Lagrangiano efectivo en QED y lagrangiano de Born-Infeld]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Bretón]]></surname>
<given-names><![CDATA[N]]></given-names>
</name>
<xref ref-type="aff" rid="A01"/>
</contrib>
</contrib-group>
<aff id="A01">
<institution><![CDATA[,Cinvestav-IPN Departamento de Física ]]></institution>
<addr-line><![CDATA[México D.F]]></addr-line>
<country>MÉXICO</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>08</month>
<year>2007</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>08</month>
<year>2007</year>
</pub-date>
<volume>53</volume>
<fpage>10</fpage>
<lpage>16</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_arttext&amp;pid=S0035-001X2007001000004&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_abstract&amp;pid=S0035-001X2007001000004&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_pdf&amp;pid=S0035-001X2007001000004&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="es"><p><![CDATA[Se presenta el lagrangiano propuesto por Born e Infeld para electrodinámica no lineal. Para mostrar su semejanza con el lagrangiano efectivo en QED, este se obtiene por el método más cercano a la derivación hecha por Weisskopf en 1936.]]></p></abstract>
<abstract abstract-type="short" xml:lang="en"><p><![CDATA[The aim of this contribution is to establish a comparison between the nonlinear electrodynamics lagrangian by Born and Infeld and the effective lagrangian in QED that describes the vacuum polarization. It is shown that the dependence in the invariants is the same in the limit of weak constant electromagnetic fields.]]></p></abstract>
<kwd-group>
<kwd lng="es"><![CDATA[Electrodinámica no lineal]]></kwd>
<kwd lng="es"><![CDATA[electrodinámica cuántica]]></kwd>
<kwd lng="en"><![CDATA[Nonlinear electrodynamics]]></kwd>
<kwd lng="en"><![CDATA[quantum electrodynamics]]></kwd>
</kwd-group>
</article-meta>
</front><body><![CDATA[ <p align="center"><font face="verdana" size="4"><b>Lagrangiano efectivo en QED y lagrangiano de Born&#150;Infeld</b></font></p>     <p align="center"><font face="verdana" size="2">&nbsp;</font></p>     <p align="center"><font face="verdana" size="2"><b>N. Bret&oacute;n</b></font></p>     <p align="center"><font face="verdana" size="2">&nbsp;</font></p>     <p align="justify"><font face="verdana" size="2"><i>Departamento de F&iacute;sica, Cinvestav&#150;IPN, Apartado Postal 14&#150;740, 07000, M&eacute;xico, D.F., M&Eacute;XICO, e&#150;mail: <a href="mailto:nora@fis.cinvestav.mx" target="_blank">nora@fis.cinvestav.mx</a></i></font></p>     <p align="justify"><font face="verdana" size="2">&nbsp;</font></p>     <p align="justify"><font face="verdana" size="2">Recibido el 1 de mayo de 2006    <br>   Aceptado el 1 de noviembre de 2006</font></p>     <p align="justify"><font face="verdana" size="2">&nbsp;</font></p>     <p align="justify"><font face="verdana" size="2"><b>Resumen</b></font></p>     ]]></body>
<body><![CDATA[<p align="justify"><font face="verdana" size="2">Se presenta el lagrangiano propuesto por Born e Infeld para electrodin&aacute;mica no lineal. Para mostrar su semejanza con el lagrangiano efectivo en QED, este se obtiene por el m&eacute;todo m&aacute;s cercano a la derivaci&oacute;n hecha por Weisskopf en 1936.</font></p>     <p align="justify"><font face="verdana" size="2"><b>Descriptores: </b>Electrodin&aacute;mica no lineal; electrodin&aacute;mica cu&aacute;ntica.</font></p>     <p align="justify"><font face="verdana" size="2">&nbsp;</font></p>     <p align="justify"><font face="verdana" size="2"><b>Abstract</b></font></p>     <p align="justify"><font face="verdana" size="2">The aim of this contribution is to establish a comparison between the nonlinear electrodynamics lagrangian by Born and Infeld and the effective lagrangian in QED that describes the vacuum polarization. It is shown that the dependence in the invariants is the same in the limit of weak constant electromagnetic fields.</font></p>     <p align="justify"><font face="verdana" size="2"><b>Keywords: </b>Nonlinear electrodynamics; quantum electrodynamics. </font></p>     <p align="justify"><font face="verdana" size="2">&nbsp;</font></p>     <p align="justify"><font face="verdana" size="2">PACS: 04.70.&#150;s; 04.70.Bw; 04.70.Dy</font></p>     <p align="justify"><font face="verdana" size="2">&nbsp;</font></p>     <p align="justify"><font face="verdana" size="2"><a href="/pdf/rmf/v53s4/v53s4a4.pdf">DESCARGAR ART&Iacute;CULO EN FORMATO PDF</a></font></p>     ]]></body>
<body><![CDATA[<p align="justify"><font face="verdana" size="2">&nbsp;</font></p>     <p align="justify"><font face="verdana" size="2"><b>References</b></font></p>     <!-- ref --><p align="justify"><font face="verdana" size="2">1. M. Born y L. Infeld, <i>Proc. Roy. Soc. Lond. A </i><b>144 </b>(1934) 425; <i>    &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=8342225&pid=S0035-001X200700100000400001&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --><!-- ref -->Proc. Roy. Soc. Lond. A </i><b>143 </b>(1934) 410; <i>    &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=8342226&pid=S0035-001X200700100000400002&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --><!-- ref -->Proc. Roy. Soc. Lond. A </i><b>147</b> (1934) 522.</font>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=8342227&pid=S0035-001X200700100000400003&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --><!-- ref --><p align="justify"><font face="verdana" size="2">2. J.F. Pleba&ntilde;ski, <i>Lecture Notes on non&#150;linear electrodynamics </i>Monograph of the Niels Bohr Institute Nordita (Copenhagen, 1968).</font>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=8342228&pid=S0035-001X200700100000400004&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --><!-- ref --><p align="justify"><font face="verdana" size="2">3. Los trabajos de Heisenberg y Euler estan en alem&aacute;n, pero es posible consultar lo mas cercano a sus desarrollos: W.S. Weisskopf, <i>Phys. Rev. </i><b>56</b> (1939) 72.</font>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=8342229&pid=S0035-001X200700100000400005&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --><!-- ref --><p align="justify"><font face="verdana" size="2">4. R.P. Feynman, <i>Space&#150;time approach to quantum electrodynamics, Phys. Rev. </i><b>76</b> (1949) 769.</font>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=8342230&pid=S0035-001X200700100000400006&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --><!-- ref --><p align="justify"><font face="verdana" size="2">5. I Schwinger, <i>Phys. Rev. </i><b>82</b> (1951) 664.</font>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=8342231&pid=S0035-001X200700100000400007&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --><!-- ref --><p align="justify"><font face="verdana" size="2">6. E. M. Lifshitz y L.P. Pitaevskii, <i>Relativistic Quantum Theory </i>Course of Theoretical Physics, (Pergamon Press, 1977). </font>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=8342232&pid=S0035-001X200700100000400008&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --><!-- ref --><p align="justify"><font face="verdana" size="2">7. A. Shabad, <i>Interaction of electromagnetic radiation with supercritical magnetic field, </i>hep&#150;th/0307214; Y.M. Cho, D.G. Pak, M.L. Walker, <i>Light propagation effects in QED: Effective action approach, Phys. Rev. D </i><b>73</b> (2006) 065014. </font>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=8342233&pid=S0035-001X200700100000400009&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --><!-- ref --><p align="justify"><font face="verdana" size="2">8. R.R. Metsaev, M.A. Rahmanov and A.A. Tseytlin, <i>Phys. Lett. B </i><b>193 </b>(1987) 207.</font>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=8342234&pid=S0035-001X200700100000400010&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --> ]]></body><back>
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