Possibly degenerate tetrad gravity and Maxwell–Dirac fields

Abstract

I present an integrated approach to tetrad gravity and Maxwell–Dirac fields, which is not singular in the case when the tetrad is degenerate. All field equations are linear. The geometric data consist only of a complex vector bundle S→M with two-dimensional fibers, where M is a real 4-manifold. All needed structures are functorially derived from S. Any considered object which is not a functorial construction is assumed to be a dynamical field.