2009•IRMA lectures in mathematics and theoretical physicsOpen access

Feynman integrals and multiple polylogarithms

Stefan Weinzierl

Abstract

In this article 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.

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Key concepts: Feynman integral, Feynman diagram, Transformation (genetics), Mathematics, Feynman graph, Algebra over a field, Physics, Mathematical physics