Conformal structures and twistors in the paravector model of spacetime

dc.contributor.authorDa Rocha, R.
dc.contributor.authorVaz, J.
dc.contributor.institutionUniversidade Estadual Paulista (Unesp)
dc.contributor.institutionUniversidade Estadual de Campinas (UNICAMP)
dc.contributor.institutionDept Math Appl
dc.description.abstractSome properties of the Clifford algebras Cl-3,Cl-0, Cl-1,Cl-3, Cl-4,Cl-1 similar or equal to C circle times Cl-1,Cl-3 and Cl-2,Cl-4 are presented, and three isomorphisms between the Dirac-Clifford algebra C circle times Cl-1,Cl-3 and Cl-4,Cl-1 are exhibited, in order to construct conformal maps and twistors, using the paravector model of spacetime. The isomorphism between the twistor space inner product isometry group SU( 2,2) and the group $pin(+)(2,4) is also investigated, in the light of a suitable isomorphism between C circle times Cl-1,Cl-3 and Cl-4,Cl-1. After reviewing the conformal spacetime structure, conformal maps are described in Minkowski spacetime as the twisted adjoint representation of $ pin(+)(2,4), acting on paravectors. Twistors are then presented via the paravector model of Clifford algebras and related to conformal maps in the Clifford algebra over the Lorentzian R-4,(1) spacetime.We construct twistors in Minkowski spacetime as algebraic spinors associated with the Dirac-Clifford algebra C circle times Cl-1,Cl-3 using one lower spacetime dimension than standard Clifford algebra formulations, since for this purpose, the Clifford algebra over R-4,R-1 is also used to describe conformal maps, instead of R-2,(4). Our formalism sheds some new light on the use of the paravector model and generalizations.en
dc.description.affiliationUniv Estadual Paulista, Inst Fis Teor, BR-01405 São Paulo, Brazil
dc.description.affiliationUniv Estadual Campinas, Inst Fis Gleb Wataghin, BR-13083970 Campinas, SP, Brazil
dc.description.affiliationDept Math Appl, IMECC, BR-60651308 Campinas, SP, Brazil
dc.description.affiliationUnespUniv Estadual Paulista, Inst Fis Teor, BR-01405 São Paulo, Brazil
dc.identifier.citationInternational Journal of Geometric Methods In Modern Physics. Singapore: World Scientific Publ Co Pte Ltd, v. 4, n. 4, p. 547-576, 2007.
dc.publisherWorld Scientific Publ Co Pte Ltd
dc.relation.ispartofInternational Journal of Geometric Methods In Modern Physics
dc.rights.accessRightsAcesso restrito
dc.sourceWeb of Science
dc.subjectconformal mapspt
dc.subjectClifford algebraspt
dc.titleConformal structures and twistors in the paravector model of spacetimeen
dcterms.rightsHolderWorld Scientific Publ Co Pte Ltd[1][2]
unesp.campusUniversidade Estadual Paulista (Unesp), Instituto de Física Teórica (IFT), São Paulopt


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