A novel approach to integration by parts reduction

TL;DR

A novel strategy constructed to overcome the limitations of currently available reduction programs based on Laporta's algorithm is presented, to construct algebraic identities from numerical samples obtained from reductions over finite fields.

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.