The torus universe in the polygon approach to (2 + 1)-dimensional gravity
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In this paper we describe the matter-free toroidal spacetime in 't Hooft's polygon approach to (2 + 1)-dimensional gravity. First we show that the constraint algebra of the polygons closes (this is a general result, not necessarily derived for a torus). Next we construct a one-polygon torus and find (in contrast to earlier results in the literature) that this slicing of spacetime is not compatible with all the solutions that emerge in the continuum formulation. Finally, we remedy this situation by adding one more polygon.
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The first discrete formulation designed explicitly for 2+1 dimensions was developed by 't Hooft et al.
“The first discrete formulation designed explicitly for 2 + 1 dimensions was developed by’ t Hooft et al. [250, 252, 253, 124, 274, 156].”
From Quantum Gravity in 2 + 1 Dimensions: The Case of a Closed Universe (2005) · cites this paper as [274]
Section 2 (p. 5) says ’t Hooft invented the polygon approach as a Hamiltonian description of 2+1-dimensional gravity, using piecewise-flat patches. It does not establish that this was the first discrete formulation designed for those dimensions. (LLM, conf=0.85)
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Research works printed but not linked: 5
- [5][5] 't Hooft G 1996 Quantization of Point Particles in 2+1 Dimensional Gravity and space-time discreteness. gr-qc/9601014 - · arXiv
- [7][7] Welling M 1996 Class. Quant. Grav. 13 653 Welling M and Bijlsma M 1996 Pauli-Lubanski Scalar in the Polygon Approach to (2+1)-Dimensional Gravity. gr-qc/9601025 Welling M 1995 Some Approaches to (2+1)-Dimensional Gravity coupled to Point Particles. hep-th/9511211 - · arXiv
- [13][13] Criscuola A and Waelbroeck H 1996 A Hamiltonian Lattice Theory for homogeneous curved Space-Times in (2+1)-Dimensions. gr-qc/9601028 Criscuola A and Waelbroeck H 1995 Quantization of (2+1) Gravity on the Torus. gr-qc/9509041 - · arXiv
- [14][14] Waelbroeck H and Zapata J A 1996 (2+1) Covariant Lattice Theory and 't Hooft's Formulation. gr-qc/9601011 - · arXiv
- [17][17] Ezawa K 1994 Phys. Rev. D 50 2935 Ezawa K 1994 Phys. Rev. D 49 5211 Ezawa K 1993 Reduced Phase Space of the First Order Einstein Gravity on R × T 2 hep-th/9312151 · arXiv
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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
- Welling, M.
- Affiliations
- Utrecht University (NL)
- Corresponding author
- Welling, M
- ORCID
- Welling, M
- Venue
- Classical and Quantum Gravity
- Publisher
- IOP Publishing
- Published
- 1997-04-01
- Volume
- 14
- Issue
- 4
- Pages
- 929-943
- ISSN
- 0264-9381 (ISSN-L)
- 1361-6382
- OpenAlex
- W2059933994
- Cited by
- 8
- References
- 0
- FWCI
- 1.24
- 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)
- Topics
- 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
- Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Black Holes and Theoretical Physics
- Keywords
- three-dimensional gravity, 't Hooft, constraint algebra, continuum limit, quantum gravity
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