Quantum dynamics of Kaluza-Klein theories
Abstract
Some of the quantum properties of Kaluza-Klein theories are studied. The classical features of these theories are reviewed, and the quantization of the gravitational field in an arbitrary number of dimensions is described. These results are then applied to a detailed analysis of the five-dimensional Kaluza-Klein model. The fifth dimension is taken to be compact and a quantum effective potential, as a function of the five-five component of the metric, is constructed. It is argued that the one-loop computation is reliable as long as the distance around the fifth dimension is large compared to the Planck length. The effective potential separates into two pieces: an induced cosmological constant, independent of the size of the fifth dimension, and a distance-dependent "Casimir" energy. The cosmological term is subtracted, leaving an attractive Casimir potential which will contract the fifth dimension to a size on the order of the Planck length. Consequences of this result are discussed and some of the ways in which it can be generalized are outlined.
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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 [4]
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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 D
- Publisher
- American Physical Society (APS)
- Published
- 1983-08-15
- Volume
- 28
- Issue
- 4
- Pages
- 772-784
- ISSN
- 0556-2821 (ISSN-L)
- OpenAlex
- W2100512262
- Cited by
- 250
- References
- 0
- Citations by year
- 2026: 3 · 2025: 3 · 2024: 2 · 2021: 2 · 2020: 9 · 2018: 6 · 2017: 3 · 2016: 4 · 2015: 5 · 2014: 5 · 2013: 4 · 2012: 5
- FWCI
- 13.36
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields (publishedVersion)
- Funders
- U.S. Department of Energy
- Yale University
- 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, quantum gravity, five-dimensional gravity, compactified extra dimensions, one-loop effective potential, Casimir energy, cosmological constant, quantum gravity corrections, higher-dimensional gravity
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