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arXiv · 2609.39540

Reconsidering the Vacuum Energy of a Massive Scalar Field in a Spherical Cavity

M. Bordag·I. G. Pirozhenko
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Abstract

We reconsider the vacuum (Casimir) energy of a massive scalar field obeying Dirichlet boundary conditions inside a spherical cavity. Using zeta-function regularization, we carefully recalculate the analytic part of the zeta function via the uniform asymptotic expansion of the modified Bessel functions. We correct a sign error present in an earlier calculation (PR D56 (1997) 4896) that affected the large-mass behavior. The renormalized vacuum energy is shown to vanish for large mass, as required on physical grounds. Numerical results reveal that the energy changes sign several times as a function of the cavity radius.

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M. Bordag, I. G. Pirozhenko. 2026-09-30. Reconsidering the Vacuum Energy of a Massive Scalar Field in a Spherical Cavity. https://arxiv.org/abs/2609.39540

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