One-Loop Correction to the Casimir Energy in Lorentz-Violating $\phi^4$ Theory with Rough Membrane Boundaries

TL;DR

This study calculates the first-order quantum correction to the Casimir energy for Lorentz-violating scalar fields with rough boundaries, using advanced renormalization and regularization techniques across different boundary conditions.

Contribution

It introduces a method to incorporate boundary effects via position-dependent counterterms in Lorentz-violating theories, extending Casimir energy calculations to rough membrane boundaries.

Findings

Radiative corrections depend on membrane roughness and boundary conditions.

The use of BSS and cutoff regularization effectively manages divergences.

Results align with theoretical expectations for Lorentz-violating scalar fields.

Abstract

In this paper, we calculate the radiative correction to the Casimir energy for both massive and massless Lorentz-violating scalar fields confined between two membranes with rough surfaces in a 3+1 dimensional spacetime. The computations are performed for four types of boundary conditions: Dirichlet, Neumann, Periodic, and Mixed. A crucial element of our approach involves the use of position-dependent counterterms to incorporate the influence of boundaries within the renormalization program. To manage the divergences that emerge in the Casimir energy calculations, we apply the Box Subtraction Scheme (BSS) along with the cutoff regularization technique. We present and discuss results for various degrees of membrane roughness, emphasizing the consistency of our findings with theoretical expectations.