Spectral geometry and SO(4) gravity in a Riemann-Cartan spacetime

Abstract

The method of coincidence limits of DeWitt is extended to autoparallels of a U 4 manifold to determine the formulae for the first three coefficients ( b 0, b 2, b 4) in the asymptotic expansion of the trace of the heat kernel of a second order laplacian-type differential operator Δ in a Riemann-Cartan spacetime. The calculation is done in the context of SO(4) gravity, with Δ acting on arbitrary spin fields transforming as scalars under the action of the coordinate transformations. The coefficients in the expansion are polynomials in certain asymptotic invariants of the metric tensor, torsion tensor, curvature tensor of the group SO(4) under which the fields transform, and their derivatives.