<?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>S0035-001X2023000500006</article-id>
<article-id pub-id-type="doi">10.31349/revmexfis.69.050703</article-id>
<title-group>
<article-title xml:lang="en"><![CDATA[Generalized equations and their solutions in the (1/2,0)+(0,1/2) representations of the Lorentz group]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Cázares]]></surname>
<given-names><![CDATA[J. A.]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Dvoeglazov]]></surname>
<given-names><![CDATA[V. V.]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Ventspils University of Appliend Sciences Faculty of Information Technologies Ventspils International Radio Astronomy Centre]]></institution>
<addr-line><![CDATA[Ventspils ]]></addr-line>
<country>Latvia</country>
</aff>
<aff id="Af2">
<institution><![CDATA[,Universidad Autónoma de Zacatecas  ]]></institution>
<addr-line><![CDATA[Zacatecas Zac.]]></addr-line>
<country>Mexico</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>10</month>
<year>2023</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>10</month>
<year>2023</year>
</pub-date>
<volume>69</volume>
<numero>5</numero>
<fpage>0</fpage>
<lpage>0</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_arttext&amp;pid=S0035-001X2023000500006&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_abstract&amp;pid=S0035-001X2023000500006&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_pdf&amp;pid=S0035-001X2023000500006&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract We present explicit examples of generalizations in relativistic quantum mechanics. First of all, we discuss the generalized spin-1/2 equations for neutrinos. They have been obtained by means of the Gersten-Sakurai method for derivations of arbitrary-spin relativistic equations. Possible physical consequences are discussed. Next, it is easy to check that both Dirac algebraic equations  D e t (   p &#94; - m ) = 0 and  D e t (   p &#94; + m ) = 0 for u - and v - 4-spinors have solutions with    p  0 = ±   E  p = ±    p  2 +   m  2. The same is true for higher-spin equations. Meanwhile, every book considers the equality    p  0 =   E  p for both u - and v - spinors of the  ( 1 / 2,0 ) &#8853; ( 0,1 / 2 ) representation, thus applying the Dirac-Feynman-Stueckelberg procedure for elimination of the negative-energy solutions. The recent Ziino works (and, independently, the articles of several others) show that the Fock space can be doubled. We re-consider this possibility on the quantum field level for both S = 1/2 and higher spin particles. The third example is: we postulate the non-commutativity of 4-momenta, and we derive the mass splitting in the Dirac equation. The applications are discussed.]]></p></abstract>
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</ref>
</ref-list>
</back>
</article>
