Photon & Axion Oscillation In a Magnetized Medium: A Covariant Treatment
  Pseudoscalar particles, with almost zero mass and very weak coupling to the visible matter, arise in many extensions of the standard model of particle physics. Their mixing with photons in the presence of an external magnetic field leads to many interesting astrophysical and cosmological consequences. This mixing depends on the medium properties, the momentum of the photon and the background magnetic field. Here we give a general treatment of pseudoscalar-photon oscillations in a background magnetic field, taking the Faraday term into account. We give predictions valid in all regimes, under the assumption that the frequency of the wave is much higher than the plasma frequency of the medium. At sufficiently high frequencies, the Faraday effect is negligible and we reproduce the standard pseudoscalar-photon mixing phenomenon. However at low frequencies, where Faraday effect is important, the mixing formulae are considerably modified. We explicitly compute the contribution due to the longitudinal mode of the photon and show that it is negligible. 
Avijit K. Ganguly, Pankaj Jain, Subhayan Mandal