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

Abstract

A short review of expansion by regions is presented. It is a well-known strategy to obtain an expansion of a given multiloop Feynman integral in a given limit where some kinematic invariants and/or masses have certain scaling measured in powers of a given small parameter. Prescriptions of this strategy are formulated in a simple geometrical language and are illustrated through simple examples.

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Notes

  1. 1.

    In fact, this step is performed within asy.m with the help of another code qhull. It is most time-consuming and can become problematic in higher-loop calculations.

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Acknowledgements

I would like to thank the organizers of the Paris Winter Workshop “The Infrared in QFT” (2–6 March 2020, Paris) and the workshop “Antidifferentiation and the Calculation of Feynman Amplitudes” (DESY Zeuthen,4–9 October 2020) for the possibility to present this talk. Supported by the Russian Science Foundation, agreement no. 21-71-30003.

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Correspondence to Vladimir A. Smirnov .

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Smirnov, V.A. (2021). Expansion by Regions: An Overview. 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_18

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  • DOI: https://doi.org/10.1007/978-3-030-80219-6_18

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