Vacuum confinement at finite temperature for scalar QED in magnetic field and deformed boundary condition

TL;DR

This paper studies the finite-temperature Casimir effect for a charged scalar field in a magnetic field with deformed boundary conditions, analyzing how temperature, magnetic field, and boundary deformation influence the Casimir energy and permeability.

Contribution

It introduces a boundary condition deformation parameter in the Casimir effect at finite temperature for scalar QED in a magnetic field, extending previous models.

Findings

Derived expressions for the Casimir free energy and permeability at various temperatures.

Analyzed the impact of boundary deformation on the Casimir effect.

Provided asymptotic formulas for permeability at low and high temperatures.

Abstract

We investigate the Casimir effect at finite temperature for a charged scalar field in the presence of an external uniform and constant magnetic field, perpendicular to the Casimir plates. We have used a boundary condition characterized by a deformation parameter $\theta$; for $\theta=0$ we have a periodic condition and for $\theta=\pi$, an antiperiodic one, for intermediate values, we have a deformation. The temperature was introduced using the imaginary time formalism and both the lagrangian and free energy were obtained from Schwinger proper time method for computing the effective action. We also computed the permeability and its asymptotic expressions for low and high temperatures.