Casimir force on a light front

TL;DR

This paper explores the Casimir force using light-front coordinates, demonstrating that such an analysis is valid and comparable to traditional equal-time approaches, thus broadening the theoretical framework for quantum vacuum interactions.

Contribution

It introduces and compares light-front coordinate analysis of the Casimir force with traditional methods, highlighting the coordinate-independence of the physical phenomenon.

Findings

Light-front analysis yields results consistent with equal-time calculations.

Coordinate choice does not affect the physical predictions of the Casimir force.

The study broadens the theoretical tools for analyzing quantum vacuum effects.

Abstract

Depending on the point of view, the Casimir force arises from variation in the energy of the quantum vacuum as boundary conditions are altered or as an interaction between atoms in the materials that form these boundary conditions. Standard analyses of such configurations are usually done in terms of ordinary, equal-time (Minkowski) coordinates. However, physics is independent of the coordinate choice, and an analysis based on light-front coordinates, where $x^+\equiv t+z/c$ plays the role of time, is equally valid. After a brief historical introduction, we illustrate and compare equal-time and light-front calculations of the Casimir force.