Module Intersection for the Integration-by-Parts Reduction of Multi-Loop Feynman Integrals
Abstract
In this manuscript, which is to appear in the proceedings of the conference "MathemAmplitude 2019" in Padova, Italy, we provide an overview of the module intersection method for the the integration-by-parts (IBP) reduction of multi-loop Feynman integrals. The module intersection method, based on computational algebraic geometry, is a highly efficient way of getting IBP relations without double propagator or with a bound on the highest propagator degree. In this manner, trimmed IBP systems which are much shorter than the traditional ones can be obtained. We apply the modern, Petri net based, workflow management system GPI-Space in combination with the computer algebra system Singular to solve the trimmed IBP system via interpolation and efficient parallelization. We show, in particular, how to use the new plugin feature of GPI-Space to manage a global state of the computation and to efficiently handle mutable data. Moreover, a Mathematica interface to generate IBPs with restricted propagator degree, which is based on module intersection, is presented in this review.
Keywords
Cite
@article{arxiv.2010.06895,
title = {Module Intersection for the Integration-by-Parts Reduction of Multi-Loop Feynman Integrals},
author = {Dominik Bendle and Janko Boehm and Wolfram Decker and Alessandro Georgoudis and Franz-Josef Pfreundt and Mirko Rahn and Yang Zhang},
journal= {arXiv preprint arXiv:2010.06895},
year = {2020}
}
Comments
19 pages, 5 figures. To appear in the proceedings of "MathemAmplitudes 2019: Intersection Theory & Feynman Integrals", held in Padova 18-20 December 2019