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

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.

Some overlaps with our works arXiv:1104.4330, arXiv:1505.00711, arXiv:1505.01044, arXiv:1505.03276. These overlaps aim to make the present paper self-contained, and do not involve the main results

References in corpus (2)

• Quantum vacuum energies and Casimir forces between partially transparent $\delta$-function plates
• Casimir Effect in the Presence of External Fields

Cited by in corpus (6)

• Local Casimir Effect for a Scalar Field in Presence of a Point Impurity
• Relative-Zeta and Casimir energy for a semitransparent hyperplane selecting transverse modes
• Local zeta regularization and the scalar Casimir effect IV. The case of a rectangular box
• Vacuum polarization with zero-range potentials on a hyperplane
• The Casimir energy anomaly for a point interaction
• A note on "Algebraic approach to Casimir force between two $\delta$-like potentials" (K. Ziemian, Ann. Henri Poincaré, Online First, 2021)