Dirac Spinors and Representations of GL(4) Group in GR
Abstract
Description
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.
LaTeXe, 7 pages; v2: text around Eq(9) and Eq(24) corrected, v3: nonsignificant improvements, one sentence in abstract slightly changed to prevent "interference" with Y. Ne'eman et al result. Anyway neither Ne'eman et al results about GL(4), nor twistors, nor loop quantum gravity, nor black hole entropy... still are not discussed here in sake of shortness
LaTeXe, 7 pages; v2: text around Eq(9) and Eq(24) corrected, v3: nonsignificant improvements, one sentence in abstract slightly changed to prevent "interference" with Y. Ne'eman et al result. Anyway neither Ne'eman et al results about GL(4), nor twistors, nor loop quantum gravity, nor black hole entropy... still are not discussed here in sake of shortness