ASYMPTOTIC BEHAVIORS OF THE HEAT KERNEL IN COVARIANT PERTURBATION-THEORY

The trace of the heat kernel is expanded in a basis of nonlocal curvat ure invariants of nth order. The coefficients of this expansion (the n onlocal form factors) are calculated to third order in the curvature i nclusive. The early-time and late-time asymptotic behaviors of the tra ce of the heat kernel are presented with this accuracy. The late-time behavior gives the criterion of analyticity of the effective action in quantum field theory. The latter point is exemplified by deriving the effective action in two dimensions.