Conformal structures and twistors in the paravector model of spacetime

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dc.creatorda Rocha, Roldao
dc.creatorVaz Jr, Jayme
dc.date2004-12-21
dc.date2007-03-06
dc.date.accessioned2026-07-07T08:19:07Z
dc.date.available2026-07-07T08:19:07Z
dc.descriptionSome properties of the Clifford algebras Cl(3,0), Cl(1,3), Cl(1,3)(C), Cl(4,1) and Cl(2,4) are presented, and three isomorphisms between the Dirac-Clifford algebra C x Cl(1,3) and Cl(4,1) 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 Spin+(2,4) is also investigated, in the light of a suitable isomorphism between C x Cl(1,3) and Cl(4,1). After reviewing the conformal spacetime structure, conformal maps are described in Minkowski spacetime as the twisted adjoint representation of Spin+(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 x Cl(1,3) using one lower spacetime dimension than standard Clifford algebra formulations, since for this purpose the Clifford algebra over R(4,1) 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.
dc.description23 pages, to be published in Int.J.Geom.Meth.Mod.Phys. 4 (4) (2007)
dc.identifierhttps://arxiv.org/abs/math-ph/0412074
dc.identifierhttp://arxiv.org/abs/math-ph/0412074
dc.identifierInt.J.Geom.Meth.Mod.Phys. 4 (2007) 547-576
dc.identifierdoi:10.1142/S0219887807002193
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/134663
dc.subjectMathematical Physics
dc.subject15A66, 53C28
dc.titleConformal structures and twistors in the paravector model of spacetime
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