Zero-point energy of massless scalar fields in the presence of soft and semihard boundaries in D dimensions

TL;DR

This paper calculates the renormalized energy density of a massless scalar field in D-dimensional flat spacetime with soft and semihard boundaries, analyzing how boundary types influence energy sign and dependence on dimensions.

Contribution

It introduces a method to compute energy densities with smoothly varying boundary potentials and compares their effects to hard boundary cases across dimensions.

Findings

Energy densities' signs depend on boundary types.

Soft and semihard boundaries alter energy dependence on D.

Comparison shows differences from traditional hard boundary results.

Abstract

The renormalized energy density of a massless scalar field defined in a D-dimensional flat spacetime is computed in the presence of "soft" and "semihard" boundaries, modeled by some smoothly increasing potential functions. The sign of the renormalized energy densities for these different confining situations is investigated. The dependence of this energy on $D$ for the cases of "hard" and "soft/semihard" boundaries are compared.