Chern-Simons quantization of (2+1)-anti-de Sitter gravity on a torus
Open accessAbstract
The Chern-Simons formulation of (2+1)-dimensional Einstein gravity with a negative cosmological constant is investigated when the spacetime has the topology . The physical phase space is shown to be a direct product of two sub-phase spaces each of which is a non-Hausdorff manifold plus a set with non-zero co-dimensions. The spacetime geometrical interpretation of each point in the phase space is also given and we explain the 1 to 2 correspondence with the ADM formalism from the geometrical viewpoint. In quantizing this theory, we construct a `modified phase space' which is a cotangent bundle on a torus. We also provide a modular invariant inner product and investigate the relation to the quantum theory which is directly related to the spinor representation of the ADM formalism.
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Only the hyperbolic-hyperbolic sector corresponds to a spacetime in which the T2 slices are spacelike.
“It may be shown that only the hyperbolic-hyperbolic sector corresponds to a spacetime in which the T2 slices are spacelike [117, 119, 182, 209].”
From Quantum Gravity in 2 + 1 Dimensions: The Case of a Closed Universe (2005) · cites this paper as [119]
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Research works printed but not linked: 7
- [5][5] S. Carlip, preprint UCD-93-15, NSF-ITP-93-63, gr-qc/9305020 · arXiv
- [7][7] W. G. Unruh and P. Newbury, preprint gr-qc/9307029 · arXiv
- [10][10] S. Carlip and J. E. Nelson, preprint DFTT 67/93, UCD-93-33, gr-qc/9311007 · arXiv
- [13][13] N. J. M. Woodhouse, Geometric Quantization (Clarendon Press, Oxford 1980)
- [15][15] G. Mess, preprint IHES/M/90/28 27 http://arxiv.org/abs/gr-qc/9305020 http://arxiv.org/abs/gr-qc/9307029 http://arxiv.org/abs/gr-qc/9311007 · arXiv
- [17][17] K. Ezawa, hep-th/9403160, to appear in Phys.Rev.D · arXiv
- [19][19] E. Witten, Comm. Math. Phys. 137 (1991) 29 28 http://arxiv.org/abs/hep-th/9403160 · arXiv
Cited by
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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
- Ezawa, K.
- Affiliations
- The University of Osaka (JP)
- Corresponding author
- Ezawa, Kiyoshi
- ORCID
- Ezawa, Kiyoshi
- Venue
- Classical and Quantum Gravity
- Publisher
- IOP Publishing
- Published
- 1995-02-01
- Volume
- 12
- Issue
- 2
- Pages
- 373-391
- ISSN
- 0264-9381 (ISSN-L)
- 1361-6382
- OpenAlex
- W1983439765
- Cited by
- 14
- References
- 0
- Citations by year
- 2020: 1 · 2013: 1
- FWCI
- 1.22
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Classical and Quantum Gravity (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- arXiv (Cornell University)
- Funders
- Japan Society for the Promotion of Science
- Topics
- Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Black Holes and Theoretical Physics
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Noncommutative and Quantum Gravity Theories
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Relativity and Gravitational Theory
- Keywords
- Chern-Simons gravity, three-dimensional gravity, anti-de Sitter space, negative cosmological constant, toroidal topology, phase space, cotangent bundle, ADM formalism, spinor representation, quantum gravity, topological gravity
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