Feynman integrals as A-hypergeometric functions
Leonardo de la Cruz · Journal of High Energy Physics · 2019
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 polynomialsg= $$ \mathcal{U} $$ U + $$ \mathcal{F} $$ F as having indeterminate coefficients. Noncompact integration cycles can be determined from the coamoeba — the argument mapping — of the algebraic variety associated withg. In general, we add a deformation togin 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.