<?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>S0035-001X2020000200180</article-id>
<article-id pub-id-type="doi">10.31349/revmexfis.66.180</article-id>
<title-group>
<article-title xml:lang="en"><![CDATA[The Frenet-Serret description of Born rigidity and its application to the Dirac equation]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Formiga]]></surname>
<given-names><![CDATA[J.B.]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Universidade Federal da Paraíba Departamento de Física ]]></institution>
<addr-line><![CDATA[João Pessoa Pb]]></addr-line>
<country>Brazil</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>04</month>
<year>2020</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>04</month>
<year>2020</year>
</pub-date>
<volume>66</volume>
<numero>2</numero>
<fpage>180</fpage>
<lpage>186</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_arttext&amp;pid=S0035-001X2020000200180&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_abstract&amp;pid=S0035-001X2020000200180&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_pdf&amp;pid=S0035-001X2020000200180&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract The role played by non-inertial frames in physics is one of the most interesting subjects that we can study when dealing with a physical theory. This is especially true for special relativity and the Dirac theory In the case of special relativity, a problem with the concept of rigidity emerged as soon as Max Born gave a reasonable definition of rigid motion: the Herglotz-Noether theorem imposes a strong restriction on the possible rigid motions. In this paper, the equivalence of this theorem with another one that is formulated with the help of Frenet-Serret formalism is proved, showing the connection between the rigid motion and the curvatures of the observer&#8217;s trajectory in spacetime. Besides, the Dirac equation in the Frenet-Serret frame for an arbitrary observer is obtained and applied to the rotating observers. The solution in the rotating frame is given in terms of that of an inertial one.]]></p></abstract>
<kwd-group>
<kwd lng="en"><![CDATA[Born rigidity]]></kwd>
<kwd lng="en"><![CDATA[accelerated frames]]></kwd>
<kwd lng="en"><![CDATA[Dirac equation]]></kwd>
<kwd lng="en"><![CDATA[rotating observers]]></kwd>
<kwd lng="en"><![CDATA[Frenet-Serret formalism]]></kwd>
<kwd lng="en"><![CDATA[03.30.+p]]></kwd>
<kwd lng="en"><![CDATA[03.65.-w]]></kwd>
<kwd lng="en"><![CDATA[02.40.-k]]></kwd>
</kwd-group>
</article-meta>
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