Quantum Gravity in 2+1 Dimensions
Abstract
This timely volume provides a broad survey of (2+1)-dimensional quantum gravity. It emphasises the 'quantum cosmology' of closed universes and the quantum mechanics of the (2+1)-dimensional black hole. It compares and contrasts a variety of approaches, and examines what they imply for a realistic theory of quantum gravity. General relativity in three spacetime dimensions has become a popular arena in which to explore the ramifications of quantum gravity. As a diffeomorphism-invariant theory of spacetime structure, this model shares many of the conceptual problems of realistic quantum gravity. But it is also simple enough that many programs of quantization can be carried out explicitly. After analysing the space of classical solutions, this book introduces some fifteen approaches to quantum gravity - from canonical quantization in York's 'extrinsic time' to Chern-Simons quantization, from the loop representation to covariant path integration to lattice methods. Relationships among quantizations are explored, as well as implications for such issues as topology change and the 'problem of time'. This book is an invaluable resource for all graduate students and researchers working in quantum gravity.
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For the torus universe, quantizing the algebra of loop variables T0 and T1 simply reproduces the theory obtained in the Chern-Simons formulation.
“For the torus universe, it is not hard to show that such a quantization simply reproduces the theory we already obtained in the Chern-Simons formulation (see, for example, Section 7.2 of [81]).”
From Quantum Gravity in 2 + 1 Dimensions: The Case of a Closed Universe (2005) · cites this paper as [81]
For a torus universe with zero or positive cosmological constant, similar constructions are possible.
“For a torus universe with zero or positive cosmological constant, similar constructions are possible.”
From Quantum Gravity in 2 + 1 Dimensions: The Case of a Closed Universe (2005) · cites this paper as [81]
In the first order formalism, Dirac quantization is equivalent to the Chern-Simons quantum theory.
“In the first order formalism, it is straightforward to show that Dirac quantization is equivalent to the Chern-Simons quantum theory we have already seen. Details can be found in Chapter 8 of [81]”
From Quantum Gravity in 2 + 1 Dimensions: The Case of a Closed Universe (2005) · cites this paper as [81]
Section 9.2 of [81] describes a partial gauge-fixing that takes advantage of the fact that every metric on a three-manifold is conformal to one of constant scalar curvature.
“Section 9.2 of [81] describes a partial gauge-fixing, which takes advantage of the fact that every metric on a three-manifold is conformal to one of constant scalar curvature.”
From Quantum Gravity in 2 + 1 Dimensions: The Case of a Closed Universe (2005) · cites this paper as [81]
Three-dimensional BF theory and its spin-foam quantization are intimately related to classical and quantum gravity in three dimensions.
“Three dimensional BF theory and the spin-foam quantization presented above is intimately related to classical and quantum gravity in three dimensions (for a classic reference see [112]).”
From The Spin-Foam Approach to Quantum Gravity (2013) · cites this paper as [112]
Riemannian three-dimensional gravity has no local degrees of freedom and is a topological theory.
“Riemannian gravity in 3 dimensions is a theory with no local degrees of freedom, i.e., a topological theory.”
From The Spin-Foam Approach to Quantum Gravity (2013) · cites this paper as [112]
Cited by
Sorted by citations
Background independent quantum gravity: a status report
Ashtekar, A., & Lewandowski, J. (2004) · Classical and Quantum Gravity · doi:10.1088/0264-9381/21/15/r01 · Cited by 1,951 · see citing works
The Spin-Foam Approach to Quantum Gravity
Perez, A. (2013) · Living Reviews in Relativity · doi:10.12942/lrr-2013-3 · Cited by 677 · see citing works
Three-dimensional loop quantum gravity: physical scalar product and spin-foam models
Noui, K., & Perez, A. (2005) · Classical and Quantum Gravity · doi:10.1088/0264-9381/22/9/017 · Cited by 181 · see citing works
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-citation
- Authors
- Carlip, S.
- Affiliations
- University of California, Davis (US)
- Corresponding author
- Carlip, Steven
- ORCID
- Carlip, Steven
- Venue
- Cambridge University Press eBooks
- Publisher
- Cambridge University Press
- Published
- 1998-07-02
- OpenAlex
- W1559981427
- Cited by
- 560
- References
- 0
- Citations by year
- 2026: 7 · 2025: 24 · 2024: 17 · 2023: 10 · 2022: 11 · 2021: 15 · 2020: 12 · 2019: 11 · 2018: 19 · 2017: 47 · 2016: 26 · 2015: 28 · 2014: 24 · 2013: 29 · 2012: 25
- FWCI
- 8.05
- Type
- book
- Language
- en
- Open access
- closed
- Locations
- Cambridge University Press eBooks (publishedVersion)
- International Linear Collider (submittedVersion)
- 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
- quantum gravity, three-dimensional gravity, quantum cosmology, closed universe, black holes, Chern-Simons gravity, loop representation, lattice methods, topology change, problem of time, canonical quantization
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