Quantization of 2+1 gravity for genus 2
Open accessAbstract
In previous papers we established and discussed the algebra of observables for 2+1 gravity at both the classical and quantum levels, and gave a systematic discussion of the reduction of the expected number of independent observables to 6g-6 (g>1). In this paper the algebra of observables for the case g=2 is reduced to a very simple form. A Hilbert space of state vectors is defined and its representations are discussed using a deformation of the Euler \ensuremath{\Gamma} function. The deformation parameter \ensuremath{\theta} depends on the cosmological and Planck's constants.
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For Λ < 0, an explicit quantization of the holonomy algebra exists for genus one and genus two, but more general results do not yet exist.
“an explicit quantization of the algebra holonomies exists for genus one (see below) and genus two [214], but more general results do not yet exist.”
From Quantum Gravity in 2 + 1 Dimensions: The Case of a Closed Universe (2005) · cites this paper as [214]
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Quantum Gravity in 2 + 1 Dimensions: The Case of a Closed Universe
Carlip, S. (2005) · Living Reviews in Relativity · doi:10.12942/lrr-2005-1 · Cited by 172 · see citing works
- Authors
- Nelson, J. E., & Regge, T.
- Affiliations
- University of Turin (IT)
- ORCID
- Nelson, J. E.
- Venue
- Physical Review D
- Publisher
- American Physical Society (APS)
- Published
- 1994-10-15
- Volume
- 50
- Issue
- 8
- Pages
- 5125-5129
- ISSN
- 0556-2821 (ISSN-L)
- OpenAlex
- W1973259124
- Cited by
- 12
- References
- 0
- FWCI
- 1.11
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields (publishedVersion)
- PubMed (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- Institutional Research Information System University of Turin (University of Turin) (submittedVersion)
- arXiv (Cornell 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
- three-dimensional gravity, quantum gravity, algebra of observables, genus 2 surfaces, topological field theory, representation theory, cosmological constant, Planck constant, Chern-Simons gravity
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