DISCRETE AND CONTINUUM APPROACHES TO THREE-DIMENSIONAL QUANTUM GRAVITY
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It is shown that, in the three-dimensional lattice gravity defined by Ponzano and Regge, the space of physical states is isomorphic to the space of gauge-invariant functions on the moduli space of flat SU(2) connections over a two-dimensional surface, which gives physical states in the ISO(3) Chern–Simons gauge theory. To prove this, we employ the q-analogue of this model defined by Turaev and Viro as a regularization to sum over states. A recent work by Turaev suggests that the q-analogue model itself may be related to an Euclidean gravity with a cosmological constant proportional to 1/k 2, where q=e 2πi/(k+2).
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In the large k limit, the Turaev-Viro Hilbert space is isomorphic to the space of gauge-invariant functions of flat SU(2) connections.
“In the large k limit, the Turaev-Viro Hilbert space is isomorphic to the space of gauge-invariant functions of flat SU(2) connections [219, 220, 242].”
From Quantum Gravity in 2 + 1 Dimensions: The Case of a Closed Universe (2005) · cites this paper as [220]
There are key differences between the formulation and the Ooguri-Crane-Yetter 4d TQFT that illuminate the relation between quantum gravity and TQFT.
“Also, it has the same structure as the Ooguri-Crane-Yetter 4d topological field theory, with a few key differences that illuminate the relation between quantum gravity and TQFT.”
From “Sum over surfaces” form of loop quantum gravity (1997) · cites this paper as [11]
The formulation has the same kinematic as the Ooguri-Crane-Yetter 4d topological field theory.
“it has the same kinematic as the Ooguri-Crane-Yetter model [10,11]”
From “Sum over surfaces” form of loop quantum gravity (1997) · cites this paper as [11]
The structure of quantum general relativity in the form presented in this paper is surprisingly similar to the Ooguri-Crane-Yetter (OCY) four dimensional topological quantum field theory.
“The structure of quantum general relativity in the form presented in this paper is surprisingly similar to the OoguriCrane-Yetter (OCY) four dimensional topological quantum field theory [10,11] a rigorously defined simplicial lattice version of four dimensional SU (2) BF theory.”
From “Sum over surfaces” form of loop quantum gravity (1997) · cites this paper as [11]
BF theory and simplicial GR are theories with crossing symmetric vertices.
“BF theory [11] and simplicial GR [8,9] are theories of this kind, and have crossing symmetric vertices.”
From “Sum over surfaces” form of loop quantum gravity (1997) · cites this paper as [11]
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Cites
Quantum Theory of Angular Momentum
Варшалович, Д. А., Moskalev, A. N., & Khersonskii, V. K. (1988) · WORLD SCIENTIFIC eBooks · doi:10.1142/0270 · Cited by 3,835 · see citing works
Quantum Theory Of Angular Momemtum
Варшалович, Д. А., Moskalev, A. N., & Khersonskii, V. K. (1988) · Cited by 3,060 · see citing works
State sum invariants of 3-manifolds and quantum 6j-symbols
Turaev, V. G., & Viro, O. Y. (1992) · Topology · doi:10.1016/0040-9383(92)90015-a · Cited by 1,145 · see citing works
Spectroscopic and Group Theoretical Methods in Physics
Blin-Stoyle, R. J. (1969) · Physics Bulletin · doi:10.1088/0031-9112/20/9/009 · Cited by 213 · see citing works
Spectroscopic and Group Theoretical Methods in Physics
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Conformal Field Theory and Solvable Lattice Models
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Quantum invariants of 3-manifold and a glimpse of shadow topology
Turaev, V. (1992) · Lecture notes in mathematics · doi:10.1007/bfb0101203 · Cited by 43 · see citing works
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Research works printed but not linked: 2
- [8]8. M. Jimbo, Lett. Math. Phys. 10 (1985) 63; V.G. Drinfeld, ' Quantum Groups ,' in Proc. Intl. Congress of Mathematicians , Berkeley, California, (1986) p.798.
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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
Barrett, J. W., & Naish-Guzman, I. (2009) · Classical and Quantum Gravity · doi:10.1088/0264-9381/26/15/155014 · Cited by 131 · see citing works
Ooguri, H. (1992) · Nuclear Physics B · doi:10.1016/0550-3213(92)90188-h · Cited by 76 · see citing works
Self-citationPerez, A., & Pranzetti, D. (2010) · Classical and Quantum Gravity · doi:10.1088/0264-9381/27/14/145009 · Cited by 53 · see citing works
- Authors
- OOGURI, H., & SASAKURA, N.
- Affiliations
- Kyoto University (JP)
- Venue
- Modern Physics Letters A
- Publisher
- World Scientific Pub Co Pte Lt
- Published
- 1991-12-21
- Volume
- 06
- Issue
- 39
- Pages
- 3591-3600
- ISSN
- 0217-7323 (ISSN-L)
- 1793-6632
- OpenAlex
- W2099064295
- Cited by
- 77
- References
- 7
- Citations by year
- 2026: 1 · 2025: 3 · 2024: 1 · 2023: 5 · 2021: 3 · 2020: 2 · 2017: 1 · 2015: 2 · 2014: 2 · 2012: 1
- FWCI
- 6.69
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Modern Physics Letters A (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- CaltechAUTHORS (California Institute of Technology) (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 quantum gravity, lattice gravity, Ponzano-Regge model, q-analogues, moduli spaces, gauge-invariant states, Euclidean gravity, cosmological constant
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