Feynman Integral: Harnessing it through Intersection Theory
Abstract: Feynman integrals are an integral part of the computation of scattering amplitudes and related quantities. The Feynman integrals obey linear relations, which are exploited by employing the standard Integration-by-parts identities to simplify the evaluation of scattering amplitudes: they can be used both for decomposing the scattering amplitudes in terms of a basis of functions, referred to as master integrals (MIs) and for the evaluation of the latter using the differential equation. I will show that they are better understood by using the Intersection Numbers, which act as scalar products between the vector spaces of the Feynman Integrals. Application to few Feynman integrals at one- and two-loops will be shown, thereby sketching various direct decomposition of Feynman integrals using multivariate Intersection numbers.
*Wednesday, 24th May 2022, 14:30 — Sala Wataghin *