Finite temperature Casimir effect for charged massless scalars in a magnetic field

TL;DR

This paper uses zeta function regularization to analyze the finite temperature Casimir effect for a charged massless scalar field between parallel plates under a magnetic field, deriving exact expressions for free energy and pressure.

Contribution

It provides exact, all-order expressions for the Casimir effect in a magnetic field at finite temperature, valid across a wide range of parameters.

Findings

Derived simple analytic formulas for free energy and pressure.

Results valid for high temperature, small plate distance, and strong magnetic field.

Expressions are accurate for nearly all parameter values.

Abstract

The zeta function regularization technique is used to study the finite temperature Casimir effect for a charged and massless scalar field confined between parallel plates and satisfying Dirichlet boundary conditions at the plates. A magnetic field perpendicular to the plates is included. Three equivalent expressions for the zeta function are obtained, which are exact to all orders in the magnetic field strength, temperature and plate distance. These expressions of the zeta function are used to calculate the Helmholtz free energy of the scalar field and the pressure on the plates, in the case of high temperature, small plate distance and strong magnetic field. In all cases, simple analytic expressions are obtained for the free energy and pressure which are accurate and valid for practically all values of temperature, plate distance and magnetic field.