Path integral study of the Casimir effect in a chiral medium

The Casimir effect is a remarkable macroscopic feature of QED, while recent lattice studies have also shown its potential nontrivial consequences in QCD. In light of having a better understanding of the Casimir effect, it is advantageous to have a self-contained path integral formulation of the phenomenon. I will show how the Casimir effect between two uncharged plates in the presence of a chiral medium, modeled with an axion term θF͂μvFμv, can be formulated in terms of the path integral, and how such a formulation leads to a 3D effective action of the restricted electromagnetic field.

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 a=a(t) in a strong magnetic field. As is known, the assumption a=a(t) is common under astrophysical conditions. In the third part of the paper, we consider the implications by instead assuming an axion amplitude a(z) depending on one coordinate z 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.