Star products and perturbative quantum field theory

TL;DR

This paper explores how deformation quantization and star products underpin perturbative quantum field theory, deriving Feynman rules and scattering functions through a novel mathematical framework.

Contribution

It demonstrates that Wick's theorem and Feynman rules naturally emerge from the structure of star products in deformation quantization.

Findings

Derived the scattering function for a free scalar field with a spacetime-dependent source.

Showed that Wick's theorem follows from star product structures.

Reproduced known operator formalism relations using deformation quantization.

Abstract

We discuss the application of the deformation quantization approach to perturbative quantum field theory. We show that the various forms of Wick's theorem are a direct consequence of the structure of the star products. We derive the scattering function for a free scalar field in interaction with a spacetime-dependent source. We show that the translation to operator formalism reproduces the known relations which lead to the derivation of the Feynman rules.