Lie algebras for the Dirac–Clifford ring

descriptionPublicationkeyboard_double_arrow_right Article 01 May 1993 English Publisher:AIP PublishingJournal:Journal of Mathematical Physics, volume 34, pages 2,066-2,074 (issn: 0022-2488, eissn: 1089-7658,

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Authors: Mignaco, Juan Alberto; Linhares, Cesar Augusto;

doi: 10.1063/1.530156

Lie algebras for the Dirac–Clifford ring

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Abstract

It is shown in general that the Dirac–Clifford ring formed by the Dirac matrices and all their products, for all even and odd space–time dimensions D, span the commutation algebras su(2D/2) for even D and su(2(D−1)/2)⊕su(2(D−1)/2) for odd D. Some physical consequences of these results are discussed herein.

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Keywords

Clifford algebras, spinors, commutation algebras, Dirac matrices, Dirac-Clifford ring, Lie algebras of Lie groups, Model quantum field theories, unitary algebras

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