Group structure of the integration-by-part identities and its application to the reduction of multiloop integrals

TL;DR

This paper explores the algebraic structure of IBP identities to streamline the reduction process of multiloop integrals, demonstrating that Lorentz-invariance identities are redundant.

Contribution

It introduces a Lie-algebraic framework to reduce the number of IBP equations and shows LI identities do not add new information.

Findings

Lie-algebraic structure simplifies IBP reduction

LI identities are redundant for integral reduction

Reduced IBP system accelerates multiloop calculations

Abstract

The excessiveness of integration-by-part (IBP) identities is discussed. The Lie-algebraic structure of the IBP identities is used to reduce the number of the IBP equations to be considered. It is shown that Lorentz-invariance (LI) identities do not bring any information additional to that contained in the IBP identities, and therefore, can be discarded.