Light front Casimir effect at finite temperature

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 et al. Phys. Rev. D 87, 065028 (2013); Chabysheva and Hiller, Phys. Rev. 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. 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.

Casimir force on a light front

“…However, physics is independent of the coordinate choice, and an analysis based on light-front coordinates [12,13,14,15,16,17,18], where x + ≡ t + z/c plays the role of time, is equally valid. This review provides a survey of applications of light-front coordinates to the Casimir force [19,20,21,22] and compares the results with equal-time calculations for a massless scalar field with boundaries fixed by parallel plates. Extensions to other fields, such as photons, is straightforward.…”