Spinor fields and the GL(4,R) gauge structure in the nonsymmetric theory of gravitation

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Abstract
The spinor structure associated with the local gauge group GL(4,R) of the nonsymmetric gravitation theory (NGT) is based on a spinor wave equation constructed from a vierbein, a GL(4,R) spin connection, and the infinite‐dimensional irreducible representations of the universal covering group S L (4,R) of the noncompact group SL(4,R). The multiplicity‐free irreducible representations of S L (4,R) correspond to bivalued spinorial representations of SL(4,R) that contain an infinite number of half‐odd integer spin particles. By adjoining the translations T4, the extended group A=T4×GL(4,R) replaces the Poincaré group P. The properties of the mass spectrum are obtained from an infinite‐component wave equation and the physical spinor field consists of an infinite sum of finite, nonunitary representations of the Lorentz group.

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