Transport equation for the photon Wigner operator in non-commutative QED

TL;DR

This paper derives a gauge-covariant quantum transport equation for the photon Wigner operator in non-commutative QED, connecting quantum dynamics with classical thermal effects and perturbative high-temperature calculations.

Contribution

It presents the first exact gauge-covariant quantum equation of motion for the photon Wigner operator in non-commutative QED, linking quantum and classical descriptions.

Findings

The transport equation captures hard thermal effects in non-commutative QED.

Leading order solutions reproduce perturbative Green amplitudes at high temperature.

The method provides a direct way to connect quantum equations with thermal field theory results.

Abstract

We derive an exact quantum equation of motion for the photon Wigner operator in non-commutative QED, which is gauge covariant. In the classical approximation, this reduces to a simple transport equation which describes the hard thermal effects in this theory. As an example of the effectiveness of this method we show that, to leading order, this equation generates in a direct way the Green amplitudes calculated perturbatively in quantum field theory at high temperature.