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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Bibliographic Details
Published inJournal of physics. A, Mathematical and theoretical Vol. 48; no. 15; pp. 153001 - 35
Main Author Henn, Johannes M
Format Journal Article
LanguageEnglish
Published United States IOP Publishing 17.04.2015
Subjects
Chen iterated integrals
Differential equations
elliptic functions
Feynman integrals
Integrals
Lectures
Mathematical analysis
Mathematical models
MATHEMATICS AND COMPUTING
multiple polylogarithms
Optimization
periods
Representations
Singularities
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Summary: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.
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SC0009988
USDOE Advanced Research Projects Agency - Energy (ARPA-E)
ISSN:1751-8113
1751-8121
DOI:10.1088/1751-8113/48/15/153001