Feynman integrals as A-hypergeometric functions

DOI10.1007/JHEP12(2019)123zbMATH Open1431.81061arXiv1907.00507MaRDI QIDQ2303191

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Publication date: 2 March 2020

Published in: (Search for Journal in Brave)

Abstract: We show that the Lee-Pomeransky parametric representation of Feynman integrals can be understood as a solution of a certain Gel'fand-Kapranov-Zelevinsky (GKZ) system. In order to define such GKZ system, we consider the polynomial obtained from the Symanzik polynomials $g=mathcalU+mathcalF$ as having indeterminate coefficients. Noncompact integration cycles can be determined from the coamoeba---the argument mapping---of the algebraic variety associated with $g$. In general, we add a deformation to $g$ in order to define integrals of generic graphs as linear combinations of their canonical series. We evaluate several Feynman integrals with arbitrary non-integer powers in the propagators using the canonical series algorithm.

Full work available at URL: https://arxiv.org/abs/1907.00507

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