Quantum Effects in Kaluza-Klein Theories
Abstract
The phenomenon of dimensional reduction in quantum theories of gravity is studied. In the five-dimensional Kaluza-Klein model, the one-loop effective potential as a function of ${g}_{55}$ is computed. When the distance around the fifth dimension is larger than the Planck length, the loop expansion is reliable. The result leads to a force tending to make the fifth dimension contract to a size on the order of the Planck length. This can be interpreted as a gravitational version of the Casimir effect in electrodynamics.
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Almost all studies of Casimir energy in Kaluza-Klein and string-theoretic contexts assume the size of extra dimensions is time-independent, primarily to identify static stable vacua.
“Almost all of these studies assume that the size of the extra dimensions is time-independent, primarily because their objective is to identify static stable vacua.”
From Stress-energy tensor of a scalar field on a product spacetime with a time-dependent compact dimension (2026) · cites this paper as [3]
Similar to the d=3 case, the 0th order Casimir terms match known time-independent results.
“Similar to the d = 3 case, the 0-th order Casimir terms match known time-independent results [3][4][5][6][7][8].”
From Stress-energy tensor of a scalar field on a product spacetime with a time-dependent compact dimension (2026) · cites this paper as [3]
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Weinberg, S. (1983) · Physics Letters B · doi:10.1016/0370-2693(83)91281-9 · Cited by 173 · see citing works
Paul, A., & Paban, S. (2026) · Journal of High Energy Physics · doi:10.1007/jhep09(2026)188
- Authors
- Appelquist, T., & Chodos, A.
- Affiliations
- Yale University (US)
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 1983-01-17
- Volume
- 50
- Issue
- 3
- Pages
- 141-145
- ISSN
- 0031-9007 (ISSN-L)
- OpenAlex
- W1969158612
- Cited by
- 318
- References
- 0
- Citations by year
- 2026: 2 · 2025: 6 · 2024: 3 · 2023: 5 · 2022: 3 · 2021: 5 · 2020: 30 · 2019: 2 · 2018: 3 · 2017: 2 · 2016: 4 · 2015: 3 · 2014: 7 · 2013: 3 · 2012: 7
- FWCI
- 40.74
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Physical Review Letters (publishedVersion)
- Topics
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Noncommutative and Quantum Gravity Theories
- Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Black Holes and Theoretical Physics
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Relativity and Gravitational Theory
- Keywords
- Kaluza-Klein theory, dimensional reduction, quantum gravity, one-loop effective potential, fifth dimension, Planck length, Casimir effect, compactification, loop expansion
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