Feynman integrals and multiple polylogarithms

Abstract

In this talk I review the connections between Feynman integrals and multiple polylogarithms. After an introductory section on loop integrals I discuss the Mellin-Barnes transformation and shuffle algebras. In a subsequent section multiple polylogarithms are introduced. Finally, I discuss how certain Feynman integrals evaluate to multiple polylogarithms.

Comments: 23 pages, talk given at the workshop "Renormalization and Galois theories", Marseille, March 2006; v2: references added