The Symmetries and the General Harmonic Solution to Equations of Maxwell Electrodynamics with an Axion
The effective Lagrangian is derived and a group of hidden symmetries is determined for Maxwell’s theory with an axion in the stationary case. The general harmonic solution is constructed, and it is shown that a central source can have only a Coulomb-type magnetic field. The electric field of such a source has a complex potential, which can be finite everywhere with a special choice of parameters. The differential scattering cross section of the test particle on a dione with an axionic charge is calculated within the first order of the perturbation theory.