Feynman Integral: The role of Intersection Theory

by Manoj Kumar Mandal (INFN - National Institute for Nuclear Physics)

Tuesday 1 Jun 2021, 11:30 → 12:30 Europe/Zurich

https://fisica-unimi.zoom.us/j/93801268810?pwd=NHB5c2N3aVhFVlNSSllGeWNLNUxCQT09

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.

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