Feynman integrals and difference equations

Abstract

We report on the calculation of multi-loop Feynman integrals for single-scale problems by means of difference equations in Mellin space. The solution to these difference equations in terms of harmonic sums can be constructed algorithmically over difference fields, the so-called Pi-Sigma-fields. We test the implementaion of the Mathematica package Sigma on examples from recent higher order perturbative calculations in Quantum Chromodynamics.

11 pages latex, 2 figures, Proceedings of the 11th International Workshop on Advanced Computing and Analysis Techniques in Physics Research (ACAT 07), Amsterdam, The Netherlands