On Clifford Subalgebras, Spacetime Splittings and Applications

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dc.creatorda Rocha, Roldao
dc.creatorVaz Jr, Jayme
dc.date2006-05-03
dc.date.accessioned2026-07-07T10:22:28Z
dc.date.available2026-07-07T10:22:28Z
dc.descriptionZ2-gradings of Clifford algebras are reviewed and we shall be concerned with an alpha-grading based on the structure of inner automorphisms, which is closely related to the spacetime splitting, if we consider the standard conjugation map automorphism by an arbitrary, but fixed, splitting vector. After briefly sketching the orthogonal and parallel components of products of differential forms, where we introduce the parallel [orthogonal] part as the space [time] component, we provide a detailed exposition of the Dirac operator splitting and we show how the differential operator parallel and orthogonal components are related to the Lie derivative along the splitting vector and the angular momentum splitting bivector. We also introduce multivectorial-induced alpha-gradings and present the Dirac equation in terms of the spacetime splitting, where the Dirac spinor field is shown to be a direct sum of two quaternions. We point out some possible physical applications of the formalism developed.
dc.description22 pages, accepted for publication in International Journal of Geometric Methods in Modern Physics 3 (8) (2006)
dc.identifierhttps://arxiv.org/abs/math-ph/0605009
dc.identifierhttp://arxiv.org/abs/math-ph/0605009
dc.identifierInt.J.Geom.Meth.Mod.Phys.3:1359-1380,2006
dc.identifierdoi:10.1142/S0219887806001661
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/175525
dc.subjectMathematical Physics
dc.subjectHigh Energy Physics - Theory
dc.subject15A66, 81Q05
dc.titleOn Clifford Subalgebras, Spacetime Splittings and Applications
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