A General Approach to Casimir Force Problems Based on Local Reflection Amplitudes and Huygen's Principle

TL;DR

This paper introduces a universal method for calculating Casimir forces using local reflection amplitudes and Huygen's principle, applicable to diverse geometries and boundary conditions.

Contribution

It presents a generalizable framework for Casimir force calculations based on local reflection amplitudes, extending applicability to various fields and geometries.

Findings

Successfully applied to uniaxial boundary conditions in parallel-plate cavities

Provides a unified approach adaptable to different geometries and boundary conditions

Enhances the theoretical toolkit for Casimir force analysis

Abstract

In this paper we describe an approach to Casimir Force problems that is ultimately generalizable to all fields, boundary conditions, and cavity geometries. This approach utilizes locally defined reflection amplitudes to express the energy per unit area of any Casimir interaction. To demonstrate this approach we solve a number of Casimir Force problems including the case of uniaxial boundary conditions in a parallel-plate cavity.