Applying Groebner Bases to Solve Reduction Problems for Feynman Integrals
高能物理 - 格点
2009-11-11 v4 高能物理 - 唯象学
高能物理 - 理论
数学物理
math.MP
摘要
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.
引用
@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}
}
备注
19 pages, uses axodraw.sty, was intended for hep-th, but, by mistake, was submitted to hep_lat