Casimir effect within D=3+1 Maxwell-Chern-Simons electrodynamics

TL;DR

This paper investigates the Casimir effect in a Lorentz-violating extended electrodynamics with a Chern-Simons term, deriving the energy spectrum, correcting previous results, and constraining the Chern-Simons parameter based on experimental data.

Contribution

It provides a new calculation of the Casimir force correction in Maxwell-Chern-Simons electrodynamics, correcting prior work and establishing experimental bounds on the Chern-Simons term.

Findings

The correction to the Casimir force is attractive and quadratic in the Chern-Simons term.

The vacuum instability vanishes at small plate separations.

The results constrain the magnitude of the Chern-Simons parameter.

Abstract

Within the framework of the (3+1)-dimensional Lorentz-violating extended electrodynamics including the CPT-odd Chern-Simons term, we consider the electromagnetic field between the two parallel perfectly conducting plates. We find the one-particle eigenstates of such a field, as well as the implicit expression for the photon energy spectrum. We also show that the tachyon-induced vacuum instability vanishes when the separation between the plates is sufficiently small though finite. In order to find the leading Chern-Simons correction to the vacuum energy, we renormalize and evaluate the sum over all one-particle eigenstate energies using the two different methods, the zeta function technique and the transformation of the discrete sum into a complex plane integral via the residue theorem. The resulting correction to the Casimir force, which is attractive and quadratic in the Chern-Simons term, disagrees with the one calculated in [M.Frank and I.Turan, Phys.Rev.D 74, 033016(2006)], using the misinterpreted equations of motion. Compared to the experimental data, our result places a constraint on the absolute value of the Chern-Simons term.