Calculation of superpropagators in non-linear quantum field theories

Abstract

A new method of constructing the superpropagators, i.e. the Fourier transforms of the expressions of the form\(\sum\limits_{n = 1}^\infty {c_n \Delta _F^n (x)} \) is suggested. The method makes it possible to derive by use of the same technique explicit analytic expressions for the superpropagators for a wide class of field theories — from strictly local up to essentially non-local. The essence of the method is the construction of a differential equation for the superpropagator which in general is of an infinite order. By use of the boundary condition atp 2=0 we find the solution of this equation depending on one arbitrary real parameter. Simple examples are given to illustrate the method.