The Casimir effect in light-front quantization

TL;DR

This paper demonstrates that the Casimir force between stationary conducting plates can be accurately computed using light-front quantization, emphasizing the importance of boundary conditions and energy density definitions.

Contribution

It provides a novel approach to calculating the Casimir effect in light-front quantization with a careful treatment of boundary conditions and energy density.

Findings

Standard Casimir force can be derived in light-front quantization.

Boundary conditions are crucial for correct results.

Using ordinary energy density yields the standard Casimir result.

Abstract

We show that the standard result for the Casimir force between conducting plates at rest in an inertial frame can be computed in light-front quantization. This is not the same as light-front analyses where the plates are at "rest" in an infinite momentum frame. In that case, Lenz and Steinbacher have shown that the result does not agree with the standard result for plates at rest. The two important ingredients in the present analysis are a careful treatment of the boundary conditions, inspired by 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.