Applying Groebner Bases to Solve Reduction Problems for Feynman Integrals
High Energy Physics - Lattice
2009-11-11 v4 High Energy Physics - Phenomenology
High Energy Physics - Theory
Mathematical Physics
math.MP
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
Cite
@article{arxiv.hep-lat/0509187,
title = {Applying Groebner Bases to Solve Reduction Problems for Feynman Integrals},
author = {A. V. Smirnov and V. A. Smirnov},
journal= {arXiv preprint arXiv:hep-lat/0509187},
year = {2009}
}
Comments
19 pages, uses axodraw.sty, was intended for hep-th, but, by mistake, was submitted to hep_lat