Comparative quantizations of (2+1)-dimensional gravity
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We compare three approaches to the quantization of (2+1)-dimensional gravity with a negative cosmological constant: reduced phase-space quantization with the York time slicing, quantization of the algebra of holonomies, and quantization of the space of classical solutions. The relationships among these quantum theories allow us to define and interpret time-dependent operators in the ``frozen time'' holonomy formulation.
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Hamilton's equations from the Poisson brackets reproduce the time dependence (42) of the moduli.
“It may be shown that the version of Hamilton’s equations of motion coming from these brackets reproduces the time dependence (42) of the moduli; see [87, 135] for details.”
From Quantum Gravity in 2 + 1 Dimensions: The Case of a Closed Universe (2005) · cites this paper as [87]
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Cites
2 + 1 dimensional gravity as an exactly soluble system
Witten, E. (1988) · Nuclear Physics B · doi:10.1016/0550-3213(88)90143-5 · Cited by 2,562 · see citing works
Role of Conformal Three-Geometry in the Dynamics of Gravitation
York, J. W. (1972) · Physical Review Letters · doi:10.1103/physrevlett.28.1082 · Cited by 1,392 · see citing works
Time in quantum gravity: An hypothesis
Rovelli, C. (1991) · Physical Review D · doi:10.1103/physrevd.43.442 · Cited by 445 · see citing works
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Research works printed but not linked: 9
- [16][16] S. Carlip, 'Six Ways to Quantize (2+1)-Dimensional Gravity,' Davis preprint UCD93-15, to appear in Proc. of the Fifth Canadian Conference on General Relativity and Relativistic Astrophysics . -
- [17][17] K. Ezawa, 'Transition Amplitude in (2+1)-Dimensional Chern-Simons Gravity on a Torus,' Osaka preprint OU-TH-179 (1992). -
- [21][21] K. Ezawa, 'Reduced Phase Space of the First Order Einstein Gravity on I R × T 2 , Osaka preprint OU-HET-185 (1993). -
- [22][22] S. Carlip, 'Geometric Structures and Loop Variables in (2+1)-Dimensional Gravity,' in Knots and Quantum Gravity , ed. J. Baez (Clarendon Press, Oxford, 1994). -
- [24][24] W. Abikoff, The Real Analytic Theory of Teichm¨ uller Space , Lecture Notes in Mathematics 820 (Springer-Verlag, Berlin, 1980). -
- [26][26] G. Mess, 'Lorentz Spacetimes of Constant Curvature,' Institut des Hautes Etudes Scientifiques preprint IHES/M/90/28 (1990). -
- [28][28] K. Ezawa, 'Addendum to 'Classical and Quantum Evolutions of the de Sitter and Anti-de Sitter Universes in 2+1 Dimensions,' ' Osaka preprint OU-HET-183-ADD (1994). -
- [34][34] A. Ashtekar and A. Magnon, Proc. Roy. Soc. (London) A346 , 375 (1975). -
- [35][35] C. Crnkovic and E. Witten, in Three Hundred Years of Gravity , ed. S. W. Hawking and W. Israel (Cambridge University Press, Cambridge, 1987). -
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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
Self-citationCarlip, S. (2023) · Reports on Progress in Physics · doi:10.1088/1361-6633/acceb4 · Cited by 41 · see citing works
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- Authors
- Carlip, S., & Nelson, J. E.
- Affiliations
- University of California, Davis (US)
- University of Turin (IT)
- Venue
- Physical Review D
- Publisher
- American Physical Society (APS)
- Published
- 1995-05-15
- Volume
- 51
- Issue
- 10
- Pages
- 5643-5653
- ISSN
- 0556-2821 (ISSN-L)
- OpenAlex
- W2094471587
- Cited by
- 31
- References
- 3
- Citations by year
- 2024: 3 · 2023: 1 · 2022: 1 · 2021: 1 · 2019: 2 · 2016: 1 · 2015: 1
- FWCI
- 1.95
- 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)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- Institutional Research Information System University of Turin (University of Turin) (submittedVersion)
- arXiv (Cornell University)
- Funders
- National Science Foundation
- U.S. Department of Energy (FG0391ER40674)
- 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, negative cosmological constant, reduced phase space quantization, time-dependent operators
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