Feynman integrals as A-hypergeometric functions

Understand

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 $g=\mathcal{U}+\mathcal{F}$ 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.