Position space equations for generic Feynman graphs

Abstract

We propose an extension of the position space approach to Feynman integrals from the banana family to generic Feynman diagrams. Our approach is based on omitting integration in position space and then writing differential equations for the products of propagators defined for any graph. We employ the so-called ‘bananization’, where we start with simple Feynman graphs and further substitute each edge with a multiple one. We explain how the previously developed theory of banana diagrams can be used to describe what happens to the differential equations on Feynman diagrams after this transformation. Our approach works for generic (large enough) dimension and masses. We expect that after Fourier transform our equations should be related to the Picard-Fuchs equations. Therefore, we describe the challenges of the Fourier transform that arise in our approach.