Séminaire de Physique Théorique

Feynman Integrals and Intersection Theory

by Prof. Pierpaolo Mastrolia (Universita degli Studi di Padova)

Europe/Paris
Amphithéâtre Léon Motchane (IHES)

Amphithéâtre Léon Motchane

IHES

35, route de Chartres, F-91440 Bures-sur-Yvette (France)
Description

I will show that Intersection Theory (for twisted de Rham cohomology) rules the algebra of Feynman integrals. In particular I will address the problem of the direct decomposition of Feynman integrals into a basis of master integrals, showing that it can by achieved by projection, using intersection numbers for differential forms. After introducing a few basic concepts of intersection theory, I will show the application of this novel method, first, to special mathematical functions, and, later, to Feynman integrals on the maximal cuts, also explaining how differential equations and dimensional recurrence relations for master Feynman integrals can be directly built by means of intersection numbers. The presented method exposes the geometric structure beneath Feynman integrals, and offers the computational advantage of bypassing the system-solving strategy characterizing the standard reduction algorithms, which are based on integration-by-parts identities. Examples of applications to multi-loop graphs contributing to multiparticle scattering, involving both massless and massive particles are presented.

Organized by

Thibault Damour

Contact
Your browser is out of date!

Update your browser to view this website correctly. Update my browser now

×