Zilch vortical effect, Berry phase, and kinetic theory

Abstract

Rotating photon gas exhibits a chirality separation along the angular velocity which is manifested through a generation of helicity and zilch currents. In this paper we study this system using the corresponding Wigner function and construct elements of the covariant chiral kinetic theory for photons from first principles. The Wigner function is solved order-by-order in ħ and the unconstrained terms are fixed by matching with quantum field theory results. We further consider the zilch and helicity currents and show that both manifestations of the chirality transport originate in the Berry phase of photons similarly to other chiral effects. Constructing the kinetic description from the Wigner function we find that the frame vector needed to fix the definition of spin of a massless particle is, in fact, the vector of the residual gauge freedom for the free Maxwell theory. We also briefly comment on the possible relation between vortical responses in rotating systems of massless particles and the anomalies of underlying quantum field theory.

Wigner functions and quantum kinetic theory of polarized photons

“…Although two results agree, the free function U appearing in ref. [55] is uniquely fixed in the present calculation, which further clarifies the physical picture underlying these results.…”

“…Notably, as opposed to the approach of solving the Wigner function from the equations of motion in ref. [55], here the Wigner function is explicitly derived as an expectation value of the corresponding operator in the quantum field theory. Although two results agree, the free function U appearing in ref.…”

“…The primary purpose of this section is to reproduce the CVE/ZVE for photons found in the previous literature such as ref. [55] to ensure the validity of our formalism. We may now utilize G h< µν to evaluate the CS currents for polarized photons,…”

“…In ref. [55], the Wigner functions of polarized photons and corresponding CVE and ZVE have been recently investigated. However, the Wigner functions were derived from the mixture of right and left-handed polarized photons via Maxwell's equations and gauge constraints therein.…”

“…We also compute the photonic CVE and ZVE in local thermal equilibrium and confirm that our results are consistent with the previous results in refs. [8,9,55]. By using the real-time formalism and adopting a specific power counting scheme, we further construct the general form of the effective QKT for polarized photons with the collision term characterized by self-energies, similar to the fermionic case in ref.…”