Casimir Effect for a Massive Scalar Field in Lorentz-Violating Aether Compactification

TL;DR

This paper explores how Lorentz symmetry breaking and extra-dimensional compactification influence the Casimir effect, revealing tunable attractive or repulsive forces and potential stabilization mechanisms in higher-dimensional quantum field theories.

Contribution

It introduces a novel analysis of the Casimir effect incorporating Lorentz-violating aether fields and quasiperiodic boundary conditions, deriving explicit formulas and exploring their physical implications.

Findings

The parameter β controls the transition between attractive and repulsive Casimir forces.

Lorentz-violating parameter α_φ amplifies the vacuum interaction significantly.

High compactification leads to a force plateau, aiding system stabilization.

Abstract

This work investigates the influence of Lorentz symmetry breaking, introduced by an aether-like field $\alpha_\phi$, on the Casimir effect within a five-dimensional flat spacetime. By considering a quasiperiodic condition regulated by the parameter $\beta$ and an extra dimension compactified at scale $b$, we derive closed-form expressions for the Casimir energy and the resulting force between two parallel plates under Neumann boundary conditions. Our results demonstrate that $\beta$ acts as a crucial control parameter, enabling a continuous transition between attractive and repulsive regimes, with a characteristic symmetry around $\beta = 0.5$. We show that the Lorentz-violating parameter $\alpha_\phi$ functions as an enhancement factor, significantly amplifying the vacuum interaction, while the geometric ratio $a/b$ proves decisive for system stabilization. Specifically, we find that the high-compactification regime leads to a plateau in the Casimir force, effectively stabilizing the interaction. Furthermore, we analyze the mass spectrum of the field, recovering standard geometric forms in the massless limit and demonstrating that while light fields ($M \ll 1$) exhibit subtle quadratic corrections, heavy fields ($M \gg 1$) lead to an exponential suppression of the Casimir effect. The interplay between Lorentz violation and extra-dimensional compactification provides a rich mechanism with potential applications in the modulation of vacuum-induced interactions at micro and nano scales.