Possibly degenerate tetrad gravity and Maxwell-Dirac fields

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.