Light front Casimir effect at finite temperature

TL;DR

This paper investigates the Casimir effect at finite temperature using light front formalism, emphasizing the importance of boundary conditions at fixed Minkowski times for correct physical results.

Contribution

It demonstrates that imposing periodic boundary conditions at fixed Minkowski times yields expected energy and entropy behaviors, clarifying issues with light front quantization at finite temperature.

Findings

Correct boundary conditions recover expected Casimir energy density.

Casimir entropy decreases linearly with temperature in the classical limit.

Unphysical boundary conditions violate Kirchhoff's theorem.

Abstract

The correct description of the standard Casimir effect for periodic boundary conditions via light front formalism implies in these conditions imposed at fixed Minkowski times [Almeida {\it et al.} Phys. Rev. {\bf D 87}, 065028 (2013); Chabysheva and Hiller, Phys. Rev. {\bf D 88}, 085006 (2013)] instead of fixed light front times. The unphysical nature of this latter condition is manifested in the vacuum part by no regularization yielding a finite Casimir energy density [Lenz and Steinbacher, Phys. Rev. {\bf D 67}, 045010 (2003)]. In the present paper, we extend this discussion and analyze the problem of the light front quantization with simultaneous presence of a thermal bath and boundary conditions. Considering both the oblique light front as well as Dirac light front coordinates, we show that the imposition of periodic boundary conditions at fixed Minkowski times recovers the expected behaviors for the energy density and Casimir entropy. We also investigate how the unphysical nature of the periodic boundary conditions imposed at fixed light front times manifests in the thermal part of the energy and entropy, showing that in the classical limit the Casimir entropy decreases linearly with the temperature (not becoming independent of the temperature as expected), and also that the Kirchhoff theorem is not respected.