Applying Groebner Bases to Solve Reduction Problems for Feynman Integrals

Preprint

20 January 2006

preprint
Published by arXiv in arXiv

https://doi.org/10.48550/arXiv.hep-lat/0509187

Abstract

We describe how Groebner bases can be used to solve the reduction problem for Feynman integrals, i.e. to construct an algorithm that provides the possibility to express a Feynman integral of a given family as a linear combination of some master integrals. Our approach is based on a generalized Buchberger algorithm for constructing Groebner-type bases associated with polynomials of shift operators. We illustrate it through various examples of reduction problems for families of one- and two-loop Feynman integrals. We also solve the reduction problem for a family of integrals contributing to the three-loop static quark potential.

Keywords

SOLVE THE REDUCTION
PROBLEM FOR FEYNMAN
FEYNMAN INTEGRALS
APPLYING GROEBNER
REDUCTION PROBLEM
GROEBNER BASES
INTEGRALS
ALGORITHM

All Related Versions

Version 1, 2005-09-30, ArXiv
Version 2, 2005-10-03, ArXiv
Version 3, 2005-10-05, ArXiv
Version 4, 2006-01-20, ArXiv
Published version: Journal of High Energy Physics, 2006 (01), 001.

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