A special irreducible matrix representation of the real Clifford algebra C(3,1)

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dc.creatorScharnhorst, K.
dc.date1997-12-11
dc.date1998-11-24
dc.date.accessioned2026-07-07T11:36:10Z
dc.date.available2026-07-07T11:36:10Z
dc.description4x4 Dirac (gamma) matrices (irreducible matrix representations of the Clifford algebras C(3,1), C(1,3), C(4,0)) are an essential part of many calculations in quantum physics. Although the final physical results do not depend on the applied representation of the Dirac matrices (e.g. due to the invariance of traces of products of Dirac matrices), the appropriate choice of the representation used may facilitate the analysis. The present paper introduces a particularly symmetric real representation of 4x4 Dirac matrices (Majorana representation) which may prove useful in the future. As a byproduct, a compact formula for (transformed) Pauli matrices is found. The consideration is based on the role played by isoclinic 2-planes in the geometry of the real Clifford algebra C(3,0) which provide an invariant geometric frame for it. It can be generalized to larger Clifford algebras.
dc.description23 pages LaTeX, to appear in the J. Math. Phys. (v2: appendix B on Pauli matrices and references are added, minor other changes)
dc.identifierhttps://arxiv.org/abs/hep-th/9712113
dc.identifierhttp://arxiv.org/abs/hep-th/9712113
dc.identifierJ.Math.Phys.40:3616-3631,1999
dc.identifierdoi:10.1063/1.532912
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/198829
dc.subjectHigh Energy Physics - Theory
dc.subjectMathematical Physics
dc.titleA special irreducible matrix representation of the real Clifford algebra C(3,1)
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