Expressions for the zeta-function regularized Casimir energy
Abstract
The expansion of the Casimir energy for a scalar field with mass m, in a space where one dimension has been compactified into a circle of length a, leads to a double-infinite series that can be regularized by analytic continuation in the space dimension. The dimensionally regularized sum is then expressed as a power series in am by means of zeta-function expansions. The two possibilities of odd and even space dimensions are distinguished. In the odd space dimension we give a power expansion for small am, in addition to the asymptotic behavior. For the even space dimension, an expansion valid for any value of am is obtained. The contribution of higher-order terms is studied and, for the three-dimensional space, results for different values of the compactification length are shown.
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The Epstein-Hurwitz zeta function ζ(s,α) is finite for Re(s)>1/2 and divergent elsewhere.
“The Epstein-Hurwitz zeta function ζ (s, α) is finite for Re(s) > 1 2 and divergent elsewhere.”
From Stress-energy tensor of a scalar field on a product spacetime with a time-dependent compact dimension (2026) · cites this paper as [9]
Zeta regularization yields an analytic continuation of the Epstein-Hurwitz zeta function.
“Zeta regularization yields the following analytic continuation [9]”
From Stress-energy tensor of a scalar field on a product spacetime with a time-dependent compact dimension (2026) · cites this paper as [9]
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Paul, A., & Paban, S. (2026) · Journal of High Energy Physics · doi:10.1007/jhep09(2026)188
- Authors
- Elizalde, E., & Romeo, A.
- Affiliations
- Universitat de Barcelona (ES)
- Department of Structure and Constituents of Matter, Faculty of Physics, University of Barcelona, Diagonal 647, 08028 Barcelona, Spain
- ORCID
- Elizalde, E.
- Venue
- Journal of Mathematical Physics
- Publisher
- AIP Publishing
- Published
- 1989-05-01
- Volume
- 30
- Issue
- 5
- Pages
- 1133-1139
- ISSN
- 0022-2488 (ISSN-L)
- 1089-7658
- OpenAlex
- W1966606706
- Cited by
- 95
- References
- 0
- Citations by year
- 2026: 1 · 2025: 1 · 2024: 1 · 2023: 1 · 2022: 4 · 2021: 3 · 2020: 2 · 2019: 1 · 2018: 1 · 2017: 2 · 2016: 6 · 2014: 2 · 2013: 5 · 2012: 2
- FWCI
- 1.59
- Type
- journal article
- Language
- en
- Update notices
- correction (1990-03-01)
- Open access
- closed
- Locations
- Journal of Mathematical Physics (publishedVersion)
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Electrodynamics and Casimir Effect
- Physical Sciences › Mathematics › Mathematical Physics › Spectral Theory in Mathematical Physics
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Advanced Mathematical Theories and Applications
- Keywords
- Casimir energy, zeta function regularization, scalar field, analytic continuation, power series expansion, asymptotic behavior
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