Light-front analysis of the Casimir effect

TL;DR

This paper demonstrates that the Casimir effect can be accurately analyzed using light-front quantization in an inertial frame, aligning with the standard equal-time results, and clarifies the importance of boundary conditions and energy density calculations.

Contribution

It shows that the Casimir effect's standard result is reproducible in light-front quantization with proper boundary conditions and energy density considerations.

Findings

Standard Casimir result obtained in light-front quantization

Proper implementation of boundary conditions is crucial

Physics is independent of coordinate choice

Abstract

The Casimir force between conducting plates at rest in an inertial frame is usually computed in equal-time quantization, the natural choice for the given boundary conditions. We show that the well-known result obtained in this way can also be obtained in light-front quantization. This differs from a light-front analysis where the plates are at "rest" in an infinite momentum frame, rather than an inertial frame; in that case, as shown by Lenz and Steinbacher, the result does not agree with the standard result. As is usually done, the analysis is simplified by working with a scalar field and periodic boundary conditions, in place of the complexity of quantum electrodynamics. The two key ingredients are a careful implementation of the boundary conditions, following the work of Almeida et al. on oblique light-front coordinates, and computation of the ordinary energy density, rather than the light-front energy density. The analysis demonstrates that the physics of the effect is independent of the coordinate choice, as it must be.