Group invariants for Feynman diagrams

TL;DR

This paper explores the use of polynomial invariants of symmetry groups in Feynman diagrams to improve understanding and evaluation strategies, especially in multi-loop quantum electrodynamics calculations.

Contribution

It introduces a polynomial basis of invariants of diagram symmetry groups in Feynman-Schwinger parameter space, aiding in diagram analysis and evaluation.

Findings

Polynomial invariants help identify symmetries in Feynman diagrams.

Invariants facilitate the evaluation of multi-loop amplitudes.

The approach is motivated by quantum electrodynamics applications.

Abstract

It is well-known that the symmetry group of a Feynman diagram can give important information on possible strategies for its evaluation, and the mathematical objects that will be involved. Motivated by ongoing work on multi-loop multi-photon amplitudes in quantum electrodynamics, here I will discuss the usefulness of introducing a polynomial basis of invariants of the symmetry group of a diagram in Feynman-Schwinger parameter space.