Casimir energy of finite width mirrors: renormalization, self-interaction limit and Lifshitz formula

TL;DR

This paper investigates the Casimir energy for finite width mirrors using a scalar field model, deriving interactions, connecting to Lifshitz theory, and addressing self-energy renormalization.

Contribution

It introduces a field theoretical approach to finite width mirrors, deriving mirror interactions, linking to Lifshitz formula, and providing a method for finite self-energy without normalization.

Findings

Derived interaction between finite width mirrors.

Established correspondence with Lifshitz formula.

Constructed a limiting procedure for finite self-energy.

Abstract

We study the field theoretical model of a scalar field in presence of spacial inhomogeneities in form of one and two finite width mirrors (material slabs). The interaction of the scalar field with the defect is described with position-dependent mass term. Within this model we derive the interaction of two finite width mirrors, establish the correspondence of the model to the Lifshitz formula and construct limiting procedure to obtain finite self-energy of a single mirror without any normalization condition.