A novel approach to integration by parts reduction

By A. Manteuffel, Robert M. Schabinger. arXiv.org, 2014

335 citations recorded by the source corpus.

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.

Subfields: Computer Networks and Communications, Hardware and Architecture

View Paper: https://www.semanticscholar.org/paper/8e0df8bc12fa3cc7eed0ca91e2c1567bd676ca7c

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computer Networks and Communications

In Hardware and Architecture

Citations in the corpus

Ultraviolet properties of N=8 supergravity at five loops (2018, methodology): “elimination and finite-field methods [79]; we used the”
Scattering amplitudes over finite fields and multivariate functional reconstruction (2016, methodology): “se nite elds under the hood for solving problems such as polynomial factorization and Greatest Common Divisor (GCD). The application of nite elds in highenergy physics has also been suggested in ref. [24], in the context of Integration-By-Parts (IBPs). However, to the best of our knowledge, an appli”
Collider physics at the precision frontier (2020, methodology): “everal massive particles involved, the algebraic linear systems start to become intractable. This led to important new developments, suggesting to perform the IBP reduction numerically over nite elds [467]. Tools which are useful to perform such a reduction are FiniteFlow [447, 468] and FireFly [469”