Asymptotic Series of Quantum Field Theory and Their Summation

Abstract

The problem of investigation of ultraviolet asymptotics in quantum field theory has met recently with specific difficulties related to the asymptotic character of power expansions of quantum perturbation theory. This article is a review on the present status of this problem. First, we discuss the saddle-point method for the path integral, by which many important results have been obtained in the last years. Then a sketch of results is given concerning the asymptotic series in problems of quantum field theory and quantum mechanics. Next we consider the problem of “summation” of such series, which arises in attempting to reach the region of not small values of the coupling constant g.