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In an optically active medium, such as a plasma that contains a neutrinobackground, the left-handed and right-handed polarization photon modes acquiredifferent dispersion relations. We study the propagation of photons in such amedium, which is otherwise isotropic, within the framework of the covariantcollissionless Boltzmann equation incorporating a term that parametrizes theoptical activity. Using the linear response approximation, we obtain theformulas for the components of the photon polarization tensor, expressed interms of integrals over the momentum distribution function of the backgroundparticles. The main result here is the formula for the P- and CP-breakingcomponent of the photon polarization tensor in terms of the parameter involvedin the new term we consider in the Boltzmann equation to describe the effectsof optical activity. We discuss the results for some particular cases, such aslong-wavelength and non-relativistic limits, for illustrate purposes. We alsodiscuss the generalizations of the P- and CP-breaking term we included in theBoltzmann equation. In particular we consider the application to a plasma witha neutrino background and establish contact with calculations of the photonself-energy in those systems in the framework of Thermal Field Theory.

Kinetic theory formulation of the $P$- and $CP$-odd terms in the photon self-energy in a medium