Universal deformation of particle momenta space in perturbation theory

TL;DR

This paper introduces a universal embedding of complex momenta and masses into a projective space, revealing a holonomic D-module structure associated with Feynman integrals, which advances the mathematical understanding of perturbative quantum field theory.

Contribution

It constructs a natural universal embedding of momenta space into a projective space and identifies a holonomic D-module structure for Feynman integrals, providing new mathematical tools.

Findings

Explicit generators for the D-module are quadratic in derivatives.

The embedding is natural with respect to properties of Feynman integrals.

A holonomic D-module exists on the physical momenta space.

Abstract

We define an embedding of the space of complex momenta and masses in perturbation theory into a universal projective space. This embedding is natural in the sense of properties of the vector bundle defined by Feynman integrals on the complement to Landau varieties. We point out that there is a holonomic D-module associated with individual Feynman integrals. We quote explicit generators for this D-module on the fully deformed space of particle momenta. This basis is quadratic in the derivatives. We conclude that there is holonomic D-module on the physical space of momenta.