{\AE}ther Coupling Effects on Casimir Energy for Self-Interacting Scalar Field within Extra Dimension

TL;DR

This paper investigates how {\

Contribution

It introduces a novel renormalization scheme for calculating thermal and radiative Casimir energy corrections in a self-interacting scalar field with {\

Findings

The total Casimir energy density is quantified with thermal and radiative effects.

The sign and magnitude of the Casimir energy depend on boundary conditions.

Results are consistent with physical expectations despite a new computational approach.

Abstract

This paper presents comprehensive calculations for thermal and first-order radiative corrections to the Casimir energy in systems involving self-interacting massive and massless scalar fields coupled with {\ae}ther in a fifth compact dimension. The method used to compute the radiative correction to the Casimir energy differs from conventional approaches by applying a unique renormalization scheme that is consistent with specific boundary conditions or backgrounds. Despite this divergence from conventional methodologies, our results demonstrate consistency within established physical limits. Furthermore, employing a toy model, we calculated the total Casimir energy density in the bulk, taking into account both thermal and radiative corrections. We also provide a thorough characterization of the total Casimir energy density in the compact dimension, detailing its magnitude and sign using graphical representations and quantitative data.