Covariant perturbation theory II. Second order in the curvature (Nucl.Phys.B)

Covariant perturbation theory proposed in the previous paper is worked up to the second order in field strengths (curvatures). The trace of the heat kernel and the one-loop effective action for the generic second-order operator are obtained with this accuracy. The calculational scheme for higher orders is presented. The large time behaviour of the trace of the heat kernel is obtained to all orders in the curvature.