The Ponzano–Regge model
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The definition of the Ponzano–Regge state-sum model of three-dimensional quantum gravity with a class of local observables is developed. The main definition of the Ponzano–Regge model in this paper is determined by its reformulation in terms of group variables. The regularization is defined and a proof is given that the partition function is well defined only when a certain cohomological criterion is satisfied. In that case, the partition function may be expressed in terms of a topological invariant, the Reidemeister torsion. This proves the independence of the definition on the triangulation of the 3-manifold and on those arbitrary choices made in the regularization. A further corollary is that when the observable is a knot, the partition function (when it exists) can be written in terms of the Alexander polynomial of the knot. Various examples of observables in S 3 are computed explicitly. Alternative regularizations of the Ponzano–Regge model by the simple cut-off procedure and by the limit of the Turaev–Viro model are discussed, giving successes and limitations of these approaches.
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The Ponzano-Regge model is well defined when natural regularizations are used.
“We will see in Part IV that natural regularizations are available and that the model is well defined [67, 281, 186].”
From The Spin-Foam Approach to Quantum Gravity (2013) · cites this paper as [67]
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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
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
Müger, M. (2003) · Journal of Pure and Applied Algebra · doi:10.1016/s0022-4049(02)00248-7 · Cited by 354 · see citing works
Topology-changing amplitudes in 2 + 1 dimensional gravity
Witten, E. (1989) · Nuclear Physics B · doi:10.1016/0550-3213(89)90591-9 · Cited by 350 · see citing works
A MODEL OF THREE-DIMENSIONAL LATTICE GRAVITY
BOULATOV, D. V. (1992) · Modern Physics Letters A · doi:10.1142/s0217732392001324 · Cited by 326 · see citing works
Invariants of piecewise-linear 3-manifolds
Barrett, J. W., & Westbury, B. W. (1996) · Transactions of the American Mathematical Society · doi:10.1090/s0002-9947-96-01660-1 · Cited by 325 · see citing works
Self-citationThree-Dimensional Quantum Gravity, Chern-Simons Theory, and the A-Polynomial
Gukov, S. (2005) · Communications in Mathematical Physics · doi:10.1007/s00220-005-1312-y · Cited by 276 · see citing works
Ponzano–Regge model revisited: III. Feynman diagrams and effective field theory
Freidel, L., & Livine, E. R. (2006) · Classical and Quantum Gravity · doi:10.1088/0264-9381/23/6/012 · Cited by 266 · see citing works
Ponzano–Regge model revisited: I. Gauge fixing, observables and interacting spinning particles
Freidel, L., & Louapre, D. (2004) · Classical and Quantum Gravity · doi:10.1088/0264-9381/21/24/002 · Cited by 218 · see citing works
Skein theory and Turaev-Viro invariants
Roberts, J. (1995) · Topology · doi:10.1016/0040-9383(94)00053-0 · Cited by 190 · see citing works
Barrett, J. W., & Westbury, B. W. (1999) · Advances in Mathematics · doi:10.1006/aima.1998.1800 · Cited by 174 · see citing works
Self-citationDiffeomorphisms and spin foam models
Freidel, L., & Louapre, D. (2003) · Nuclear Physics B · doi:10.1016/s0550-3213(03)00306-7 · Cited by 155 · see citing works
Asymptotics of 6 <i>j</i> and 10 <i>j</i> symbols
Freidel, L., & Louapre, D. (2003) · Classical and Quantum Gravity · doi:10.1088/0264-9381/20/7/303 · Cited by 113 · see citing works
Racah Algebra for an Arbitrary Group
Derome, J.-R., & Sharp, W. T. (1965) · Journal of Mathematical Physics · doi:10.1063/1.1704698 · Cited by 105 · see citing works
DISCRETE AND CONTINUUM APPROACHES TO THREE-DIMENSIONAL QUANTUM GRAVITY
OOGURI, H., & SASAKURA, N. (1991) · Modern Physics Letters A · doi:10.1142/s0217732391004140 · Cited by 77 · see citing works
Ooguri, H. (1992) · Nuclear Physics B · doi:10.1016/0550-3213(92)90188-h · Cited by 76 · cited 1× · see citing works
“The main idea of the argument is given in [25, 27, 28], though the details of the sign factors given here are new.”
BackgroundPonzano-Regge model revisited II: Equivalence with Chern-SimonsPreprint
Freidel, L., & Louapre, D. (2004) · arXiv (Cornell University) · doi:10.48550/arxiv.gr-qc/0410141 · Cited by 74 · see citing works
Semiclassical limits of simplicial quantum gravity
Barrett, J. W., & Foxon, T. J. (1994) · Classical and Quantum Gravity · doi:10.1088/0264-9381/11/3/009 · Cited by 65 · see citing works
Self-citationTopological field theory and the quantum double of SU(2)
Bais, F. A., & Muller, N. M. (1998) · Nuclear Physics B · doi:10.1016/s0550-3213(98)00572-0 · Cited by 57 · see citing works
Observables in the Turaev-Viro and Crane-Yetter models
Barrett, J. W., Martins, J. F., & García-Islas, J. M. (2007) · Journal of Mathematical Physics · doi:10.1063/1.2759440 · Cited by 56 · see citing works
Self-citationGeometrical measurements in three-dimensional quantum gravity
Barrett, J. W. (2003) · International Journal of Modern Physics A · doi:10.1142/s0217751x03017981 · Cited by 53 · see citing works
Self-citationSPIN NETWORKS AND KNOT POLYNOMIALS
Kauffman, L. H. (1990) · International Journal of Modern Physics A · doi:10.1142/s0217751x90000039 · Cited by 46 · see citing works
Major, S. (1999) · American Journal of Physics · doi:10.1119/1.19175 · Cited by 44 · see citing works
The Turaev-Viro state sum model and three-dimensional quantum gravity
Archer, F. J., & Williams, R. M. (1991) · Physics Letters B · doi:10.1016/0370-2693(91)90295-2 · Cited by 44 · see citing works
Quantum invariants of links and 3-valent graphs in 3-manifolds
Turaev, V. G. (1993) · Publications mathématiques de l IHÉS · doi:10.1007/bf02699190 · Cited by 37 · see citing works
A combinatorial approach to topological quantum field theories and invariants of graphs
Karowski, M., & Schrader, R. (1993) · Communications in Mathematical Physics · doi:10.1007/bf02096773 · Cited by 34 · see citing works
Non abelian Reidemeister torsion and volume form on the SU(2)-representation space of knot groups
Dubois, J. (2005) · Annales de l’institut Fourier · doi:10.5802/aif.2136 · Cited by 28 · see citing works
The equality of 3-manifold invariants
Barrett, J. W., & Westbury, B. W. (1995) · Mathematical Proceedings of the Cambridge Philosophical Society · doi:10.1017/s0305004100073825 · Cited by 28 · see citing works
Self-citationNon Abelian Twisted Reidemeister Torsion for Fibered Knots
Dubois, J. (2006) · Canadian Mathematical Bulletin · doi:10.4153/cmb-2006-006-0 · Cited by 27 · see citing works
Skein spaces and spin structures
BARRETT, J. W. (1999) · Mathematical Proceedings of the Cambridge Philosophical Society · doi:10.1017/s0305004198003168 · Cited by 26 · see citing works
Self-citationTopology change in (2+1)-dimensional gravity
Carlip, S., & Cosgrove, R. (1994) · Journal of Mathematical Physics · doi:10.1063/1.530760 · Cited by 26 · see citing works
Lattice Chern-Simons gravity via the Ponzano-Regge model
Kawamoto, N., NIELSEN, H. B., & Sato, N. (1999) · Nuclear Physics B · doi:10.1016/s0550-3213(99)00331-4 · Cited by 20 · see citing works
FEYNMAN LOOPS AND THREE-DIMENSIONAL QUANTUM GRAVITY
Barrett, J. W. (2005) · Modern Physics Letters A · doi:10.1142/s0217732305017743 · Cited by 15 · see citing works
Self-citationNew Proof of the Cheeger–Müller Theorem
Braverman, M. (2003) · Annals of Global Analysis and Geometry · doi:10.1023/a:1021227705930 · Cited by 4 · see citing works
The Ponzano-Regge model and Reidemeister torsionPreprint
Barrett, J. W., & Naish-Guzman, I. (2006) · arXiv (Cornell University) · doi:10.48550/arxiv.gr-qc/0612170 · Cited by 4 · see citing works
Self-citationSum rules for SU(2) Racah coefficient from group integral
Tanimura, N., & Tanimura, O. (1991) · Journal of Mathematical Physics · doi:10.1063/1.529171 · Cited by 3 · see citing works
Flagged first, then by citations
Research works printed but not linked: 5
- [1][1] M.A. Armstrong, Basic Topology, Maidenhead: McGraw-Hill 1979. -
- [17][17] J. Moussouris, Quantum models of space-time based on recoupling theory, D. Phil thesis, St. Cross College, Oxford, 1983. -
- [19][19] C. Rourke; B. Sanderson, Introduction to piecewise-linear topology, Springer-Verlag, Berlin, 1982. -
- [25][25] Noboru Kawamoto, Holger Bech Nielsen, Noriaki Sato. Lattice ChernSimons gravity via Ponzano-Regge model, Nucl. Phys. B555 (1999) 629649, hep-th/9902165. - · arXiv
- [32][32] L. Kauffman; S. Lins, Temperley-Lieb recoupling theory and invariants of 3-manifolds, Annals of mathematics studies No. 134, Princeton University Press 1994. -
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Hu, B. L., & Verdaguer, E. (2020) · Cambridge University Press eBooks · doi:10.1017/9780511667497.018 · Cited by 4 · see citing works
Delcamp, C., & Ishtiaque, N. (2025) · Annales Henri Poincaré · doi:10.1007/s00023-025-01591-x · Cited by 3 · see citing works
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Donà, P., Haggard, H. M., Carlo Rovelli, C., Sreeram, G., & Taddei, J. (2025) · Physical review. D/Physical review. D. · doi:10.1103/68r1-pkx2 · Cited by 2 · see citing works
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Livine, E. R., & Maris, V. (2024) · Classical and Quantum Gravity · doi:10.1088/1361-6382/ad78a0 · Cited by 2 · see citing works
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Livine, E. R., & Bonzom, V. (2025) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.111.046003 · Cited by 2 · see citing works
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Livine, E. R., & Pan, Q. (2023) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.107.066001 · Cited by 1 · see citing works
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Hu, B. L., & Verdaguer, E. (2020) · Cambridge University Press eBooks · doi:10.1017/9780511667497.009 · Cited by 1 · see citing works
Goeller, C., Oriti, D., & Schmid, G. (2023) · Annales Henri Poincaré · doi:10.1007/s00023-023-01330-0 · Cited by 1 · see citing works
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Carlip, S. J. (2024) · Encyclopedia of Mathematical Physics · doi:10.1016/b978-0-323-95703-8.00256-1 · Cited by 1 · see citing works
Геометрические кручения и топологическая теория поля в стиле Атьи
Korepanov, I. G. (2009) · Теоретическая и математическая физика · doi:10.4213/tmf6323
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Hu, B. L., & Verdaguer, E. (2020) · Cambridge University Press eBooks · doi:10.1017/9780511667497.010
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Hu, B. L., & Verdaguer, E. (2020) · Cambridge University Press eBooks · doi:10.1017/9780511667497.004
- Authors
- Barrett, J. W., & Naish-Guzman, I.
- Affiliations
- University of Nottingham (GB)
- Venue
- Classical and Quantum Gravity
- Publisher
- IOP Publishing
- Published
- 2009-07-14
- Volume
- 26
- Issue
- 15
- Pages
- 155014
- ISSN
- 0264-9381 (ISSN-L)
- 1361-6382
- OpenAlex
- W2014941686
- Cited by
- 131
- References
- 34
- Citations by year
- 2026: 3 · 2025: 8 · 2024: 6 · 2023: 6 · 2022: 2 · 2021: 5 · 2020: 30 · 2019: 3 · 2018: 7 · 2016: 5 · 2015: 5 · 2014: 9 · 2013: 9 · 2012: 12
- FWCI
- 7.57
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Licence
- Locations
- Classical and Quantum Gravity (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Noncommutative and Quantum Gravity Theories
- Physical Sciences › Mathematics › Geometry and Topology › Geometric and Algebraic Topology
- Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Black Holes and Theoretical Physics
- Keywords
- Ponzano-Regge model, three-dimensional quantum gravity, state sum models, Reidemeister torsion, knot invariants, Alexander polynomial, 3-manifolds
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