PULLBACK-INVARIANT MATTER COUPLINGS TO DEGENERATE TETRADS

An algorithm is described for the construction of actions for scalar, spinor, and vector gauge fields that remains well defined when the met ric is degenerate and that involves no contravariant tensor fields. Th ese actions produce the standard matter dynamics and coupling to gravi ty when the tetrad is non-degenerate, but have the property that all f ields on a spacetime manifold M that appear in them can be pulled back to any smooth manifold M' through an arbitrary map phi : M' --> M, an d that this pullback leaves the action invariant when phi has degree o ne.