Wigner functions and quantum kinetic theory of polarized photons

Understand

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.