Revisiting the Casimir Energy with General Boundary Conditions, and applications in 1D Crystals

TL;DR

This paper derives new formulas for Casimir energy under general boundary conditions and applies them to calculate quantum vacuum energy in one-dimensional crystal models with periodic potentials.

Contribution

It introduces a general boundary condition framework for Casimir energy calculations and applies it to 1D crystal systems with periodic potentials.

Findings

New expressions for Casimir energy with general boundary conditions

Quantum vacuum energy computed for 1D crystal models

Framework applicable to various quantum field configurations

Abstract

We obtain new expressions for the Casimir energy between plates that are mimicked by the most general possible boundary conditions allowed by the principles of quantum field theory. This result enables to provide the quantum vacuum energy for scalar fields propagating under the influence of a one-dimensional crystal represented by a periodic potential formed by an infinite array of identical potentials with compact support.