Fermionic Casimir effect in an axial Lorentz-violating background

TL;DR

This paper studies how CPT-odd Lorentz-symmetry violation affects the fermionic Casimir effect between parallel plates, deriving exact mode quantization and analyzing the vacuum energy modifications due to the background vector.

Contribution

It provides a detailed analysis of the fermionic Casimir effect in the presence of Lorentz-violating axial backgrounds, including exact mode solutions and energy corrections.

Findings

Parallel components of the background do not affect the Casimir energy after renormalization.

The normal component of the background modifies the spectrum and introduces Lorentz-violating corrections.

A closed-form logarithmic integral representation for the Casimir energy is derived and analyzed.

Abstract

We investigate the fermionic Casimir effect for a Dirac field confined between two parallel plates with MIT bag boundary conditions in the presence of CPT-odd Lorentz-symmetry violation described by a constant axial background vector $b_{\mu}$. The exact mode quantization is derived from the modified Dirac equation in the planar geometry, and the vacuum energy is formulated through a phase-shift representation. For spacelike backgrounds we show that the components parallel to the plates can be absorbed into a shift of the transverse momenta and therefore do not affect the renormalized Casimir energy, while the component normal to the plates modifies the longitudinal spectrum and produces a genuine Lorentz-violating correction. Both the timelike component $b_{0}$ and the normal spacelike component $b_{z}$ can thus be treated within a unified framework characterized by a single effective spectral parameter. A closed logarithmic integral representation for the Casimir energy is obtained and its behavior is analyzed in the Lorentz-symmetric, weak-background, and strong-background regimes.