Axion Electrodynamics and the Axionic Casimir Effect

A general scheme for axion electrodynamics is given, in which a surrounding medium of constant permittivity and permeability is assumed. Then, as an application, we provide simple numerical estimates for the electromagnetic current density produced by the electrically neutral time-dependent axions <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>a</mi><mo>=</mo><mi>a</mi><mo>(</mo><mi>t</mi><mo>)</mo></mrow></semantics></math></inline-formula> in a strong magnetic field. As is known, the assumption <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>a</mi><mo>=</mo><mi>a</mi><mo>(</mo><mi>t</mi><mo>)</mo></mrow></semantics></math></inline-formula> is common under astrophysical conditions. In the third part of the paper, we consider the implications by instead assuming an axion amplitude <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>a</mi><mo>(</mo><mi>z</mi><mo>)</mo></mrow></semantics></math></inline-formula> depending on one coordinate <i>z</i> only. If such an axion field is contained within two large metal plates, one obtains an axion-generated splitting of the eigenmodes for the dispersion relation. These modes yield equal, though opposite, contributions to the pressure on the plates. We calculate the magnitude of the splitting effect in a simple one-dimensional model.