A novel approach to integration by parts reduction

TL;DR

This paper introduces a new method for integration by parts reduction in quantum field theory that leverages algebraic identities from finite field samples, aiming to improve efficiency and scalability.

Contribution

The paper presents a novel strategy that overcomes limitations of existing reduction programs by using algebraic identities derived from numerical samples over finite fields.

Findings

Method is highly parallelizable

Reduces memory footprint during reduction

Achieves significantly better run-times

Abstract

Integration by parts reduction is a standard component of most modern multi-loop calculations in quantum field theory. We present a novel strategy constructed to overcome the limitations of currently available reduction programs based on Laporta's algorithm. The key idea is to construct algebraic identities from numerical samples obtained from reductions over finite fields. We expect the method to be highly amenable to parallelization, show a low memory footprint during the reduction step, and allow for significantly better run-times.