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Holonomic Anti-Differentiation and Feynman Amplitudes

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Anti-Differentiation and the Calculation of Feynman Amplitudes

Part of the book series: Texts & Monographs in Symbolic Computation ((TEXTSMONOGR))

Abstract

Computer algebra methods within the scope of the holonomic systems approach provide a versatile toolbox to integration problems in the context of Feynman diagrams. This is demonstrated with the aid of several benchmark problems, ranging from hypergeometric series evaluations to Bessel integrals of sunrise diagrams.

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Acknowledgements

We would like to thank Johannes Blümlein and Carsten Schneider for organizing the WPC workshop on “Anti-Differentiation and the Calculation of Feynman Amplitudes” at DESY Zeuthen, despite the difficult circumstances due to the corona pandemic. We are extremely grateful to Mikhail Kalmykov for providing us with this list of challenge problems and for many references. The discussions with him during the workshop enlightened the physics background of these computational tasks.

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Authors and Affiliations

  1. Johann Radon Institute for Computational and Applied Mathematics (RICAM), Austrian Academy of Sciences, Linz, Austria

    Christoph Koutschan

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  1. Christoph Koutschan
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Correspondence to Christoph Koutschan .

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Editors and Affiliations

  1. Deutsches Elektronen-Synchrotron, DESY, Zeuthen, Germany

    Johannes Blümlein

  2. Research Institute for Symbolic Computation, Johannes Kepler University Linz, Linz, Austria

    Carsten Schneider

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Koutschan, C. (2021). Holonomic Anti-Differentiation and Feynman Amplitudes. In: Blümlein, J., Schneider, C. (eds) Anti-Differentiation and the Calculation of Feynman Amplitudes. Texts & Monographs in Symbolic Computation. Springer, Cham. https://doi.org/10.1007/978-3-030-80219-6_11

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  • DOI: https://doi.org/10.1007/978-3-030-80219-6_11

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