Background field quantization and non-commutative Maxwell theory

TL;DR

This paper develops a canonical quantization method for non-commutative Maxwell theory in background fields, deriving the Wigner function and distribution function to analyze high-temperature behavior of the theory.

Contribution

It introduces a canonical quantization approach for non-commutative Maxwell theory in background fields and derives explicit forms of the Wigner and distribution functions at high temperature.

Findings

Derived the complete basis for expansion in weak, slowly varying backgrounds.

Obtained the Wigner function governing high-temperature perturbative amplitudes.

Provided a closed-form distribution function for non-commutative U(1) gauge theory at high temperature.

Abstract

We quantize non-commutative Maxwell theory canonically in the background field gauge for weak and slowly varying background fields. We determine the complete basis for expansion under such an approximation. As an application, we derive the Wigner function which determines the leading order high temperature behavior of the perturbative amplitudes of non-commutative Maxwell theory. To leading order, we also give a closed form expression for the distribution function for the non-commutative $U (1)$ gauge theory at high temperature.