Axion Electrodynamics and the Casimir Effect

We present a concise review of selected parts of axion electrodynamics and its application to Casimir physics. We present the general formalism including the boundary conditions at a dielectric surface, derive the dispersion relation in the case where the axion parameter has a constant spatial derivative in the direction normal to the conducting plates, and calculate the Casimir energy for the simple case of scalar electrodynamics using dimensional regularization.