THE NONLOCAL STRUCTURE OF THE ONE-LOOP EFFECTIVE ACTION VIA PARTIAL SUMMATION OF THE ASYMPTOTIC-EXPANSION

We propose a new ζ-function-like prescription for the one-loop effective action which reduces the problem of summation of the asymptotic expansion to that of the analytical continuation of coefficients of the asymptotic expansion on the whole complex plane of their order. The heat kernel asymptotic expansion up to the terms of third order in rapidly varying background fields (curvatures) is calculated and the covariant nonlocal expressions for the heat kernel, the ζ-function and the one-loop effective action are obtained. © 1990.