Factorization of covariant Feynman graphs for the effective action

TL;DR

This paper proves a factorization property of covariant Feynman graphs, separating the momentum integral from background-field details, and provides a closed form for the integral using graph polynomials.

Contribution

It introduces a novel factorization of Feynman graphs in covariant perturbation theory and derives explicit expressions for the momentum integrals involved.

Findings

Factorization separates topology-dependent integrals from background-field data.

Closed-form expressions for momentum integrals using four graph polynomials.

Results applicable to both covariant and non-covariant perturbation theories.

Abstract

We prove a neat factorization property of Feynman graphs in covariant perturbation theory. The contribution of the graph to the effective action is written as a product of a massless scalar momentum integral that only depends on the basic graph topology, and a background-field dependent piece that contains all the information of spin, gauge representations, masses etc. We give a closed expression for the momentum integral in terms of four graph polynomials whose properties we derive in some detail. Our results can also be useful for standard (non-covariant) perturbation theory.