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

Understand

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.