Symmetries and solutions of field equations of axion electrodynamics

TL;DR

This paper classifies symmetries and finds exact solutions for axion electrodynamics models, revealing extended invariances, conservation laws, and solutions including superluminal propagation with positive energy density.

Contribution

It provides a comprehensive group classification, identifies special interaction cases, and constructs a broad class of exact solutions, including superluminal ones.

Findings

Extensions of Poincaré invariance for constant and exponential interactions

Derived conservation laws related to symmetries

Found exact solutions with superluminal propagation and positive energy density

Abstract

The group classification of models of axion electrodynamics with arbitrary self interaction of axionic field is carried out. It is shown that extensions of the basic Poincar\'e invariance of these models appear only for constant and exponential interactions. The related conservation laws are discussed. Using the In\"on\"u-Wigner contraction the non-relativistic limit of equations of axion electrodynamics is found. An extended class of exact solutions for the electromagnetic and axion fields is obtained. Among them there are solutions including up to six arbitrary functions. In particular, solutions which describe propagation with velocities faster than the velocity of light are found. These solutions are smooth and bounded functions which correspond to positive definite and bounded energy density.