Probing Lorentz symmetry violation via the Casimir effect in rectangular cavities

This paper investigates the Casimir effect as a probe of Lorentz symmetry violation for a real scalar field confined to a rectangular waveguide with Dirichlet boundary conditions. The authors derive modified mode spectra and vacuum energies for various configurations of a Lorentz-violating background four-vector. They show that these configurations induce anisotropic modifications of dispersion relations and that the resulting Casimir energy acquires characteristic direction-dependent corrections that encode the breaking of Lorentz symmetry. The analysis provides a framework for isolating Lorentz-violating effects in confined geometries and highlights Casimir systems as sensitive probes of anisotropic physics and fundamental spacetime symmetries.