Local zeta regularization and the scalar Casimir effect III. The case with a background harmonic potential

TL;DR

This paper applies local zeta regularization to renormalize the vacuum expectation value of the stress-energy tensor for a scalar field in a harmonic potential, advancing understanding of quantum field effects in external potentials.

Contribution

It extends the local zeta regularization framework to the case of a scalar field with a harmonic background potential, providing new renormalization results.

Findings

Renormalized vacuum expectation value of stress-energy tensor obtained.

Explicit formulas for energy in harmonic potential derived.

Framework applicable to other external potentials.

Abstract

Applying the general framework for local zeta regularization proposed in Part I of this series of papers, we renormalize the vacuum expectation value of the stress-energy tensor (and of the total energy) for a scalar field in presence of an external harmonic potential.