Applying Groebner Bases to Solve Reduction Problems for Feynman Integrals

Preprint

5 October 2005

preprint
Published by arXiv in arXiv

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
REDUCTION PROBLEM
FEYNMAN INTEGRALS
APPLYING GROEBNER
GROEBNER BASES
ALGORITHM
INTEGRALS

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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