Physics – High Energy Physics – High Energy Physics - Lattice
Scientific paper
2005-09-30
JHEP 0601 (2006) 001
Physics
High Energy Physics
High Energy Physics - Lattice
19 pages, uses axodraw.sty, was intended for hep-th, but, by mistake, was submitted to hep_lat
Scientific paper
10.1088/1126-6708/2006/01/001
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.
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