New Approximations to the Fradkin representation for Green's functions

TL;DR

This paper introduces a new variant of the Fradkin representation for Green's functions, making certain calculations more accessible, and applies it to $b4\u03b3^4$ theory, also deriving an improved Schwinger-DeWitt expansion.

Contribution

A novel variant of the Fradkin representation that simplifies calculations for Green's functions with external potentials and its application to quantum field theory.

Findings

New variant simplifies certain Green's function calculations.

Application to four-dimensional b4b3^4 theory demonstrated.

Derived an improved Schwinger-DeWitt asymptotic expansion.

Abstract

A new variant of the exact Fradkin representation of the Green's function $G_c(x,y|gU)$, defined for arbitrary external potential $U$, is presented. Although this new approach is very similar in spirit to that previously derived by Fried and Gabellini, for certain calculations this specific variant, with its prescribed approximations, is more readily utilizable. Application of the simplest of these forms is made to the $\lambda\Phi^4$ theory in four dimensions. As an independent check of these approximate forms, an improved version of the Schwinger-DeWitt asymptotic expansion of parametrix function is derived.