The Art of Computing Loop Integrals

Abstract

A perturbative approach to quantum field theory involves the computation of loop integrals, as soon as one goes beyond the leading term in the perturbative expansion. First I review standard techniques for the computation of loop integrals. In a second part I discuss more advanced algorithms. For these algorithms algebraic methods play an important role. A special section is devoted to multiple polylogarithms. I tried to make these notes self-contained and accessible both to physicists and mathematicians.

Comments: 49 pages, to appear in the proceedings of the workshop "Renormalization and Universality in Mathematical Physics", held at the Fields Institute, Toronto, October 2005