Macaulay Matrix for Feynman Integrals: Linear Relations and Intersection Numbers
High Energy Physics - Theory
2023-05-23 v2
Abstract
We elaborate on the connection between Gel'fand-Kapranov-Zelevinsky systems, de Rham theory for twisted cohomology groups, and Pfaffian equations for Feynman integrals. We propose a novel, more efficient algorithm to compute Macaulay matrices, which are used to derive Pfaffian systems of differential equations. The Pfaffian matrices are then employed to obtain linear relations for -hypergeometric (Euler) integrals and Feynman integrals, through recurrence relations and through projections by intersection numbers.
Cite
@article{arxiv.2204.12983,
title = {Macaulay Matrix for Feynman Integrals: Linear Relations and Intersection Numbers},
author = {Vsevolod Chestnov and Federico Gasparotto and Manoj K. Mandal and Pierpaolo Mastrolia and Saiei J. Matsubara-Heo and Henrik J. Munch and Nobuki Takayama},
journal= {arXiv preprint arXiv:2204.12983},
year = {2023}
}
Comments
51 page, 5 figures, matches published version