Physics

Aerospace engineering

Hypergeometric distribution

Pure mathematics

Pfaffian

Mathematics

Mathematical physics

Intersection (aeronautics)

Cohomology

Matrix (chemical analysis)

Engineering

Composite material

Materials science

Feynman diagram

Journal of High Energy Physics

A bstract 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 $$ \mathcal{A} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>A</mml:mi> </mml:math> -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