Universal deformation of particle momenta space in perturbation theory

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.