A new method for finding more symmetry relations of Feynman integrals

TL;DR

This paper presents a novel method for deriving additional symmetry relations of Feynman integrals by solving momentum transformations within rational functions, potentially reducing the complexity of integral families.

Contribution

The paper introduces a new approach that finds more symmetry relations than existing software by focusing on rational function transformations and implementing gauge conditions.

Findings

Finds more symmetry relations than current software

Reduces the number of unique sectors in integral families

Uses gauge conditions for efficient symmetry search

Abstract

We introduce a new method for deriving Feynman integral symmetry relations. By solving the ansatz of momentum transformation in the field of rational functions rather than constants, this method can sometimes find more symmetry relations, compared to some state-of-the-art software. The new method may help to further decrease the number of unique sectors in an integral family. Well-chosen gauge conditions are implemented in this method for the efficient symmetry searching.