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

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.

Some overlaps with our works arXiv:1104.4330, arXiv:1505.00711, arXiv:1505.01044, arXiv:1505.01651. These overlaps aim to make the present paper self-contained, and do not involve the main results. In comparison with version v3, reference [26] added

References in corpus (4)

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• Vacuum Stress and Closed Paths in Rectangles, Pistons, and Pistols
• On approximate solutions of semilinear evolution equations II. Generalizations, and applications to Navier-Stokes equations
• Local zeta regularization and the scalar Casimir effect III. The case with a background harmonic potential

Cited by in corpus (6)

• Local Casimir Effect for a Scalar Field in Presence of a Point Impurity
• The Dirichlet Casimir Energy For ϕ^4 Theory in a Rectangular Waveguide
• Relative-Zeta and Casimir energy for a semitransparent hyperplane selecting transverse modes
• 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)