Axions and Photons In Terms of Particles and Anti-Particles

Abstract

The axion photon system in an external magnetic field, when for example considered with the geometry of the experiments exploring axion photon mixing (which can be represented by a 1+1 effective model) displays a continuous axion-photon duality symmetry in the limit the axion mass is neglected. The conservation law that follows from this symmetry is obtained. The magnetic field interaction is seen to be equivalent to first order to the interaction of a complex charged field with an external electric potential, where this ficticious electric potential is proportional to the external magnetic field. This allows one to solve for the scattering amplitudes using already known scalar QED results. Axion photon oscillations can be understood as violations of a charge symmetry in the scalar QED language. Going beyond the linear theory, the axion photon system in a self consistent magnetic field is shown, using this formalism, to have interesting soliton solutions that represent new non gravitational ways of trapping light. Finally, generalizing the scalar QED formalism to 2+1 dimensions makes it clear that a photon and an axion splitt into two components in an inhomogeneous magnetic field, an effect that reminds us of the Stern Gerlach experiment