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PreprintCC BY 4.0arXiv

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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Cite

BibTeXRIS
BibTeX
@misc{bordag2026reconsidering,
  title = {{Reconsidering the Vacuum Energy of a Massive Scalar Field in a Spherical Cavity}},
  author = {M. Bordag and I. G. Pirozhenko},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2609.39540},
  eprint = {2609.39540},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.39540},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Reconsidering the Vacuum Energy of a Massive Scalar Field in a Spherical Cavity
AU  - M. Bordag
AU  - I. G. Pirozhenko
PY  - 2026
DA  - 2026/10/18
PB  - arXiv
DO  - 10.48550/arxiv.2609.39540
UR  - https://arxiv.org/abs/2609.39540
AB  - 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.
ER  -