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 A-hypergeometric (Euler) integrals and Feynman integrals, through recurrence relations and through projections by intersection numbers.

Macaulay Matrix for Feynman Integrals: Linear Relations and Intersection Numbers

Vsevolod Chestnov;Federico Gasparotto;Manoj K. Mandal;Pierpaolo Mastrolia;Henrik J. Munch;
2022

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 A-hypergeometric (Euler) integrals and Feynman integrals, through recurrence relations and through projections by intersection numbers.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11577/3461272
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