Functional derivation of Casimir energy at non-zero temperature

TL;DR

This paper develops a functional integration method to calculate the Casimir energy density and pressure at any temperature, extending traditional zero-temperature approaches to finite-temperature systems.

Contribution

The paper introduces a functional derivation technique for Casimir energy that seamlessly generalizes to non-zero temperature environments.

Findings

Derived expressions for Casimir energy density at various temperatures.

Provided a method applicable to finite-temperature quantum field systems.

Demonstrated the approach's effectiveness through explicit calculations.

Abstract

Performing functional integration of the free Lagrangian, we find the vacuum energy of a field. The functional integration is performed in a way which easily generalizes to systems at non-zero temperature. We use this technique to obtain the Casimir energy density and pressure at arbitrary temperatures.