On the Application of Intersection Theory to Feynman Integrals: the multivariate case
Manoj Kumar Mandal, Federico Gasparotto · 2022
This is a contribution to the proceedings of the MathemAmplitudes 2019 conference held in December 2019 in Padova, Italy and it is built upon the series of papers~\cite{Mastrolia:2018uzb, Frellesvig:2019kgj, Frellesvig:2019uqt, Frellesvig:2020qot}. In the framework of intersection theory a direct projection of any given integral in terms of a preferred basis is directly achieved, thus avoiding the traditional linear system solving procedure. The coefficients of the decomposition are expressed in terms of intersection numbers. In this contribution we review their derivation, focusing on the recursive algorithm presented in~\cite{Mizera:2019gea, Frellesvig:2019uqt}, applicable to integrals admitting a multivariate representation. This proceedings is complementary to the one by Frellesvig and Mattiazzi~\cite{Frellesvig:2021vem} concerning the univariate case. For other contributions see also~\cite{Mastrolia:mathproc,Mizera:2019ose,Weinzierl:2020gda,Brown:2020rda,Vanhove:2020qtt,Bendle:2020iim}.