Axions, Photons and Physics Beyond the Standard Model

In this thesis, we re-assess some aspects of axionic electrodynamics by coupling non-linear electromagnetic effects to axion physics. We present a number of motivations to justify the coupling of the axion to the photon in terms of a general non-linear extension of the electromagnetic sector. Our emphasis in the paper relies on the investigation of the constitutive permittivity and permeability tensors, for which the axion contribution introduces a dependence on the frequency and wave vector of the propagating radiation. Also, we point out how the axion mass and the axion-photon coupling constant contribute to a dispersive behavior of the electromagnetic waves, in contrast to what happens in the case of non-linear extensions, when effective refractive indices appear which depend only on the direction of the propagation with respect to the external fields. The axion changes this picture by yielding refractive indices with dependence on the wavelength. We apply our results to the special case of the Born-Infeld Electrodynamics and we show that it becomes birefringent whenever the axion is coupled. We also include in our analysis the Lorentz violation phenomenon through a Carroll-Field-Jackiw term, where we investigate the influence of this sector on the dispersion relations, and consequently, on the optical phenomena.