Casimir effect at finite temperature of charged scalar field

TL;DR

This paper investigates how finite temperature and external magnetic fields affect the Casimir effect for charged scalar fields, providing analytical expressions for free energy and pressure in different magnetic regimes.

Contribution

It introduces a combined analysis of finite temperature and magnetic field effects on the Casimir effect for charged scalar particles using Schwinger's method.

Findings

Casimir free energy computed for strong and weak magnetic fields

Pressure expressions derived under different magnetic regimes

Finite temperature modifies the Casimir force magnitude and sign

Abstract

The Casimir effect for Dirac as well as for scalar charged particles is influenced by external magnetic fields. It is also influenced by finite temperature. Here we consider the Casimir effect for a charged scalar field under the combined influence of an external magnetic field and finite temperature. The free energy for such a system is computed using Schwinger's method for the calculation of the effective action in the imaginary time formalism. We consider both the limits of strong and weak magnetic field in which we compute the Casimir free energy and pressure.