Asymptotic Expansions of Feynman Amplitudes in a Generic Covariant Gauge

TL;DR

This paper develops a method to analyze Feynman amplitudes in gauge theories using Symanzik polynomials and Mellin representation, extending asymptotic expansion theorems to gauge contexts for both UV and IR regimes.

Contribution

It introduces a construction of Symanzik polynomials and Mellin representation for gauge theory amplitudes in a generic covariant gauge, extending asymptotic expansion results.

Findings

Constructed Symanzik polynomials for gauge theories.

Established Mellin representation in terms of invariants.

Extended asymptotic expansion theorems to gauge theories.

Abstract

We show in this paper how to construct Symanzik polynomials and the Schwinger parametric representation of Feynman amplitudes for gauge theories in an unspecified covariant gauge. The complete Mellin representation of such amplitudes is then established in terms of invariants (squared sums of external momenta and squared masses). From the scaling of the invariants by a parameter we extend for the present situation a theorem on asymptotic expansions, previously proven for the case of scalar field theories, valid for both ultraviolet and infrared behaviors of Feynman amplitudes.