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arXiv · 2109.07584

Kinematic singularities of Feynman integrals and principal A-determinants

René Pascal Klausen
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Abstract

We consider the analytic properties of Feynman integrals from the perspective of general A-discriminants and A-hypergeometric functions introduced by Gelfand,Kapranov and Zelevinsky (GKZ). This enables us, to give a clear and mathematically rigour description of the singular locus, also known as Landau variety, via principal A-determinants. We also comprise a description of the various second type singularities. Moreover, by the Horn-Kapranov-parametrization we give a very efficient way to calculate a parametrization of Landau varieties. We furthermore present a new approach to study the sheet structure of multivalued Feynman integrals by use of coamoebas.

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René Pascal Klausen. 2021-09-15. Kinematic singularities of Feynman integrals and principal A-determinants. https://doi.org/10.1007/jhep02(2022)004

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