Wigner functions and quantum kinetic theory of polarized photons

TL;DR

This paper develops a quantum kinetic theory for polarized photons using Wigner functions, incorporating quantum corrections and side-jump effects, and verifies the theory through consistency checks with known phenomena.

Contribution

It introduces a novel quantum kinetic framework for polarized photons, including quantum corrections and side-jump effects, applicable to massless gauge bosons like gluons.

Findings

Derived Wigner functions for polarized photons in Coulomb gauge.

Identified side-jump effects for massless photons.

Constructed a quantum kinetic theory with quantum corrections.

Abstract

We derive the Wigner functions of polarized photons in the Coulomb gauge with the $\hbar$ expansion applied to quantum field theory, and identify side-jump effects for massless photons. We also discuss the photonic chiral vortical effect for the Chern-Simons current and zilch vortical effect for the zilch current in local thermal equilibrium as a consistency check for our formalism. The results are found to be in agreement with those obtained from different approaches. Moreover, using the real-time formalism, we construct the quantum kinetic theory (QKT) for polarized photons. By further adopting a specific power counting scheme for the distribution functions, we provide a more succinct form of an effective QKT. This photonic QKT involves quantum corrections associated with self-energy gradients in the collision term, which are analogous to the side-jump corrections pertinent to spin-orbit interactions in the chiral kinetic theory for massless fermions. The same theoretical framework can also be directly applied to weakly coupled gluons in the absence of background color fields.