Casimir effect within $(3{+}1)D$ Maxwell-Chern-Simons electrodynamics

Within the framework of the Lorentz-violating $(3{+}1)$-dimensional extended electrodynamics including the Lorentz-violating CPT-odd Chern-Simons term, we consider the electromagnetic field between 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. 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 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 [1] and based on wrong equations of motion. Compared with the experimental data, our result places a constraint on the absolute value of the Chern-Simons term.