Lectures on differential equations for Feynman integrals

Over the last year significant progress was made in the understanding of the computation of Feynman integrals using differential equations (DE). These lectures give a review of these developments, while not assuming any prior knowledge of the subject. After an introduction to DE for Feynman integral...

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Vydané v:Journal of physics. A, Mathematical and theoretical Ročník 48; číslo 15
Hlavný autor: Henn, Johannes M
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: IOP Publishing 17.04.2015
Predmet:
Chen iterated integrals
elliptic functions
Feynman integrals
multiple polylogarithms
periods
ISSN:1751-8113, 1751-8121
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Popis
Shrnutí:Over the last year significant progress was made in the understanding of the computation of Feynman integrals using differential equations (DE). These lectures give a review of these developments, while not assuming any prior knowledge of the subject. After an introduction to DE for Feynman integrals, we point out how they can be simplified using algorithms available in the mathematical literature. We discuss how this is related to a recent conjecture for a canonical form of the equations. We also discuss a complementary approach that is based on properties of the space-time loop integrands, and explain how the ideas of leading singularities and d-log representations can be used to find an optimal basis for the DE. Finally, as an application of these ideas we show how single-scale integrals can be bootstrapped using the Drinfeld associator of a DE.
ISSN:1751-8113
1751-8121
DOI:10.1088/1751-8113/48/15/153001