Feynman Integrals and Intersection Theory

Monday, 12 October 2020 at 11:15, in Y36 K08 - Campus Irchel

The reduction of a large number of scalar multi-loop integrals to a smaller set of Master Integrals is an integral part of the computation of any multi-loop amplitudes. Such reduction is usually achieved by solving huge systems of linear relations existing among Feynman integrals. Here we present a new way to obtain such reduction, where intersection numbers are used to project Feynman integrals directly on the set of Master Integrals, acting as a scalar product between them. Moreover we present a general algorithm for constructing multivariate intersection numbers relevant to Feynman integrals. We apply it to the derivation of contiguity relations for special functions, to the derivation of differential equations and to the decomposition of a few Feynman integrals at one- and two-loops, as first steps towards potential applications to generic multi-loop integrals.