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Dirac Spinors and Representations of GL(4) Group in GR

Alexander Yu. Vlasov
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Abstract

Transformation properties of Dirac equation correspond to Spin(3,1) representation of Lorentz group SO(3,1), but group GL(4,R) of general relativity does not accept a similar construction with Dirac spinors. On the other hand, it is possible to look for representation of GL(4,R) in some bigger space, there Dirac spinors are formally situated as some "subsystem." In the paper is described construction of such representation, using Clifford and Grassmann algebras of 4D space.

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Alexander Yu. Vlasov. 2003-04-21. Dirac Spinors and Representations of GL(4) Group in GR. https://arxiv.org/abs/math-ph/0304006

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