Casimir effect in a Lorentz-violating tensor extension of a scalar field theory

Abstract: This paper investigates the Casimir Energy modifications due to the Lorentz-violating CPT-even contribution in an extension of the scalar QED. We have considered the complex scalar field satisfying Dirichlet boundary conditions between two parallel plates separated by a small distance. An appropriate tensor parametrization allowed us to study the Casimir effect in three setups: isotropic, anisotropic parity-odd, and anisotropic parity-even. We have shown that the Lorentz-violating contributions promote increased Casimir energy for both the isotropic and anisotropic parity-odd configurations. However, in the parity-even case, the Lorentz-violating terms can promote either an increase or a decrease in the Casimir energy. We have shown that both the increased and decreased amounts in the Casimir energy depend on the momentum projection over the Lorentz-violating vectors.