Algebraic And Dirac-hestenes Spinors And Spinor Fields

dc.creatorRodrigues Jr. W.A.
dc.date2004
dc.date2015-06-26T14:25:23Z
dc.date2015-11-26T14:14:56Z
dc.date2015-06-26T14:25:23Z
dc.date2015-11-26T14:14:56Z
dc.date.accessioned2018-03-28T21:15:47Z
dc.date.available2018-03-28T21:15:47Z
dc.identifier
dc.identifierJournal Of Mathematical Physics. , v. 45, n. 7, p. 2908 - 2944, 2004.
dc.identifier222488
dc.identifier10.1063/1.1757037
dc.identifierhttp://www.scopus.com/inward/record.url?eid=2-s2.0-3543081718&partnerID=40&md5=185205b36bce2d480f3287a34b5eb164
dc.identifierhttp://www.repositorio.unicamp.br/handle/REPOSIP/94742
dc.identifierhttp://repositorio.unicamp.br/jspui/handle/REPOSIP/94742
dc.identifier2-s2.0-3543081718
dc.identifier.urihttp://repositorioslatinoamericanos.uchile.cl/handle/2250/1242656
dc.descriptionAlmost all presentations of Dirac theory in first or second quantization in physics (and mathematics) textbooks make use of covariant Dirac spinor fields. An exception is the presentation of that theory (first quantization) offered originally by Hestenes and now used by many authors. There, a new concept of spinor field (as a sum of nonhomogeneous even multivectors fields) is used. However, a careful analysis (detailed below) shows that the original Hestenes definition cannot be correct since it conflicts with the meaning of the Fierz identities. In this paper we start a program dedicated to the examination of the mathematical and physical basis for a comprehensive definition of the objects used by Hestenes. In order to do that we give a preliminary definition of algebraic spinor fields (ASF) and Dirac-Hestenes spinor fields (DHSF) on Minkowski space-time as some equivalence classes of pairs (ξu, ψu), where ξu is a spinorial frame field and ψu is an appropriate sum of multivectors fields (to be specified below). The necessity of our definitions are shown by a careful analysis of possible formulations of Dirac theory and the meaning of the set of Fierz identities associated with the bilinear covariants (on Minkowski space-time) made with ASF or DHSF. We believe that the present paper clarifies some misunderstandings (past and recent) appearing on the literature of the subject. It will be followed by a sequel paper where definitive definitions of ASF and DHSF are given as appropriate sections of a vector bundle called the left spin-Clifford bundle. The bundle formulation is essential in order to be possible to produce a coherent theory for the covariant derivatives of these fields on arbitrary Riemann-Cartan space-times. The present paper contains also Appendixes A-E which exhibits a truly useful collection of results concerning the theory of Clifford algebras (including many tricks of the trade) necessary for the intelligibility of the text. © 2004 American Institute of Physics.
dc.description45
dc.description7
dc.description2908
dc.description2944
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dc.languageen
dc.publisher
dc.relationJournal of Mathematical Physics
dc.rightsaberto
dc.sourceScopus
dc.titleAlgebraic And Dirac-hestenes Spinors And Spinor Fields
dc.typeArtículos de revistas


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