Modern Summation Methods for Loop Integrals in Quantum Field Theory: The Packages Sigma, EvaluateMultiSums and SumProduction

A large class of Feynman integrals, like e.g., two-point parameter integrals with at most one mass and containing local operator insertions, can be transformed to multi-sums over hypergeometric expressions. In this survey article we present a difference field approach for symbolic summation that ena...

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Bibliographic Details
Published inJournal of physics. Conference series Vol. 523; no. 1; pp. 12037 - 17
Main Author Schneider, C
Format Journal Article
LanguageEnglish
Published Bristol IOP Publishing 06.06.2014
Subjects
Binomials
Field theory
Harmonics
Integrals
Mathematical analysis
Operators (mathematics)
Packages
Physics
Quantum field theory
Quantum theory
Simplification
Sums
Tasks
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Summary:A large class of Feynman integrals, like e.g., two-point parameter integrals with at most one mass and containing local operator insertions, can be transformed to multi-sums over hypergeometric expressions. In this survey article we present a difference field approach for symbolic summation that enables one to simplify such definite nested sums to indefinite nested sums. In particular, the simplification is given -if possible- in terms of harmonic sums, generalized harmonic sums, cyclotomic harmonic sums or binomial sums. Special emphasis is put on the developed Mathematica packages Sigma, EvaluateMultiSums and SumProduction that assist in the task to perform these simplifications completely automatically for huge input expressions.
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ISSN:1742-6588
1742-6596
DOI:10.1088/1742-6596/523/1/012037