Thermofield Dynamics and Casimir Effect for Fermions

TL;DR

This paper extends thermofield dynamics to fermionic fields, analyzing the Casimir effect in confined geometries at finite temperature, revealing how the Casimir pressure's nature depends on geometry and temperature.

Contribution

It develops a fermionic counterpart to the bosonic formalism for thermofield dynamics and applies it to analyze the Casimir effect in fermionic systems.

Findings

Casimir pressure can be attractive or repulsive depending on edge ratios.

The sign change of Casimir pressure occurs at a specific temperature.

Estimated temperature for pressure sign change in baryonic length scales.

Abstract

A generalization of the Bogoliubov transformation is developed to describe a space compactified fermionic field. The method is the fermionic counterpart of the formalism introduced earlier for bosons (J. C. da Silva, A. Matos Neto, F. C. Khanna and A. E. Santana, Phys. Rev. A 66 (2002) 052101), and is based on the thermofield dynamics approach. We analyse the energy-momentum tensor for the Casimir effect of a free massless fermion field in a $d$-dimensional box at finite temperature. As a particular case the Casimir energy and pressure for the field confined in a 3-dimensional parallelepiped box are calculated. It is found that the attractive or repulsive nature of the Casimir pressure on opposite faces changes depending on the relative magnitude of the edges. We also determine the temperature at which the Casimir pressure in a cubic boc changes sign and estimate its value when the edge of the cybe is of the order of confining lengths for baryons.