Bosonic Casimir effect in an aether-like Lorentz-violating scenario with higher order derivatives

TL;DR

This paper explores how Lorentz-violating modifications, involving higher derivatives and a space-like vector, affect the bosonic Casimir effect, leading to significant corrections in energy and pressure depending on boundary conditions.

Contribution

It introduces a Lorentz-violating model with higher derivatives affecting the Casimir effect, highlighting the dependence on vector direction and boundary conditions.

Findings

Casimir energy and pressure are significantly altered by Lorentz violation.

Higher derivative order influences the magnitude of corrections.

The effect depends on the orientation of the Lorentz-violating vector.

Abstract

In this paper we investigate the bosonic Casimir effect in a Lorentz-violating symmetry scenario. The theoretical model adopted consists of a real massive scalar quantum field confined in a region between two large parallel plates, having its dynamics governed by a modified Klein-Gordon equation that presents a Lorentz symmetry breaking term. In this context we admit that the quantum field obeys specific boundary conditions on the plates. The Lorentz-violating symmetry is implemented by the presence of an arbitrary constant space-like vector in a CPT-even aether-like approach, considering a direct coupling between this vector with the derivative of the field in higher order. The modification on the Klein-Gordon equation produces important corrections on the Casimir energy and pressure. Thus, we show that these corrections strongly depend on the order of the higher derivative term and the specific direction of the constant vector, as well as the boundary conditions considered.