Local zeta regularization and the scalar Casimir effect IV. The case of a rectangular box

TL;DR

This paper applies local zeta regularization to compute the renormalized vacuum expectation values of observables, including the stress-energy tensor and total energy, for a massless scalar field in a rectangular box of arbitrary dimensions.

Contribution

It extends the local zeta regularization framework to arbitrary rectangular geometries for scalar fields, providing explicit calculations of physical observables.

Findings

Explicit formulas for the stress-energy tensor in rectangular boxes

Renormalized total energy expressions for scalar fields

Validation of the regularization method in arbitrary dimensions

Abstract

Applying the general framework for local zeta regularization proposed in Part I of this series of papers, we compute the renormalized vacuum expectation value of several observables (in particular, of the stress-energy tensor and of the total energy) for a massless scalar field confined within a rectangular box of arbitrary dimension.