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Feynman integrals as A-hypergeometric functions
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DOI：10.1007/JHEP12(2019)123.png)
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Abstract
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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 = U + F 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.
Keywords:
Scattering Amplitudes
Differential and Algebraic Geometry
Perturbative
QCD
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