Finite temperature Casimir effect of massive fermionic fields in the presence of compact dimensions

TL;DR

This paper analyzes the finite temperature Casimir effect for massive fermionic fields in a spacetime with compact dimensions, deriving explicit formulas for the Casimir free energy and force, and showing the force is always attractive.

Contribution

It provides explicit high and low temperature expansions of the Casimir free energy and force for fermionic fields in a spacetime with compact dimensions, revealing the force's always attractive nature.

Findings

Casimir force is always attractive at any temperature.

Explicit high and low temperature expansions of the Casimir free energy and force.

Asymptotic behavior of the Casimir force in small separation limit.

Abstract

We consider the finite temperature Casimir effect of a massive fermionic field confined between two parallel plates, with MIT bag boundary conditions on the plates. The background spacetime is $M^{p+1}\times T^q$ which has $q$ dimensions compactified to a torus. On the compact dimensions, the field is assumed to satisfy periodicity boundary conditions with arbitrary phases. Both the high temperature and the low temperature expansions of the Casimir free energy and the force are derived explicitly. It is found that the Casimir force acting on the plates is always attractive at any temperature regardless of the boundary conditions assumed on the compact torus. The asymptotic limits of the Casimir force in the small plate separation limit are also obtained.