On the Casimir energy for scalar fields with bulk inhomogeneities

TL;DR

This paper investigates the Casimir energy for a scalar field interacting with a finite inhomogeneous layer, providing calculations of the propagator, energy, and pressure, along with a renormalization approach.

Contribution

It introduces a model with position-dependent mass to analyze Casimir effects in inhomogeneous media, including detailed calculations and renormalization methods.

Findings

Derived the propagator for inhomogeneous scalar fields

Calculated Casimir energy and pressure for a finite layer

Discussed renormalization in dimensional regularization

Abstract

We study the field theoretical model of a real scalar field in presence of spacial inhomogeneity in form of a finite width mirror (material layer). The interaction of the scalar field with the defect is described with position-dependent mass term. We calculate the propagator of the theory, the Casimir energy and the pressure on the boundaries of the layer. We discuss the renormalization procedure for the model in dimensional regularization.