The DOI matches its Crossref record; 3 of the 3 references it cites were found in a registry or an index.
A MODEL OF THREE-DIMENSIONAL LATTICE GRAVITY
Open accessAbstract
A model is proposed which generates all oriented 3D simplicial complexes weighted with an invariant associated with a topological lattice gauge theory. When the gauge group is SU q (2), q n =1, it is the Turaev-Viro invariant and the model may be regarded as a nonperturbative definition of 3D simplicial quantum gravity. If one takes a finite Abelian group G, the corresponding invariant gives the rank of the first cohomology group of a complex C:I G (C)=rank(H 1 (C,G)), which means a topological expansion in the Betti number b 1 . In general, it is a theory of the Dijkgraaf-Witten type, i.e., determined completely by the fundamental group of a manifold.
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“Building on work by Boulatov [60], Freidel and Loupre have recently considered a variant of the Ponzano-Regge model, and have shown that although the sum over topologies diverges, it is Borel summable [132].”
From Quantum Gravity in 2 + 1 Dimensions: The Case of a Closed Universe (2005) · cites this paper as [60]
In the citing paper
“indeed, we know from loop quantum gravity [3,29] and from other approaches [21], that the N i 's are naturally related to the area of the faces, and their intertwiner to the volume.”
From Barrett–Crane model from a Boulatov–Ooguri field theory over a homogeneous space (2000) · cites this paper as [29]
Citations
Cites
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
Spectroscopic and Group Theoretical Methods in Physics
Bloch, F., Cohen, S. G., De-Shalit, A., Sambursky, S., & Talmi, I. (1968) · Cited by 162
Three Manifolds and Graph InvariantsPreprint
Rama, S. K., & Sen, S. (1991) · arXiv (Cornell University) · doi:10.48550/arxiv.hep-th/9112071 · Cited by 1
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Tanasă, A. (2021) · Oxford University Press eBooks · doi:10.1093/oso/9780192895493.005.0007
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Tanasă, A. (2021) · Oxford University Press eBooks · doi:10.1093/oso/9780192895493.005.0005
Tanasă, A. (2021) · Oxford University Press eBooks · doi:10.1093/oso/9780192895493.005.0001
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Tanasă, A. (2021) · Oxford University Press eBooks · doi:10.1093/oso/9780192895493.005.0003
Tanasă, A. (2021) · Oxford University Press eBooks · doi:10.1093/oso/9780192895493.005.0008
Renormalization of the Grosse–Wulkenhaar model, one-loop examples
Tanasă, A. (2021) · Oxford University Press eBooks · doi:10.1093/oso/9780192895493.005.0002
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Tanasă, A. (2021) · Oxford University Press eBooks · doi:10.1093/oso/9780192895493.005.0006
Summary of results on the diagrammatics of the coloured SYK model and of the Gurău–Witten model
Tanasă, A. (2021) · Oxford University Press eBooks · doi:10.1093/oso/9780192895493.005.0009
Collier, S., Eberhardt, L., & Zhang, M. (2023) · SciPost Physics · doi:10.21468/scipost.report.7508
Collier, S., Eberhardt, L., & Zhang, M. (2023) · SciPost Physics · doi:10.21468/scipost.report.7507
Bilson-Thompson, S. (2024) · Springer eBooks · doi:10.1007/978-3-031-43452-5_7
Multiple-order tensor field theory: Enumeration of unitary invariant observables
Geloun, J. B., & Solente, A. (2026) · Journal of Mathematical Physics · doi:10.1063/5.0291399
Géométrie des simplexes et modèles de mousses de spin
Roberto Pereira, B. (2010) · theses.fr (ABES) · doi:10.70675/4774b44cz986az4df2za56fz6fc428d82fc0
Radiative Corrections in Spinfoam Quantum Gravity
Riello, A. (2014) · theses.fr (ABES) · doi:10.70675/e80506e4z56a4z47e8z84e1z90643916a827
Tensorial methods and renormalization in Group Field Theories
Carrozza, S. (2013) · theses.fr (ABES) · doi:10.70675/452fbf63z2e27z4890z920ez05f51c70b608
Delepouve, T. (2017) · theses.fr (ABES) · doi:10.70675/59fa0739zbac3z4a54zac2fzfd528555ce8b · Cited by 1
Random Tensor models : Combinatorics, Geometry, Quantum Gravity and Integrability
Dartois, S. (2015) · theses.fr (ABES) · doi:10.70675/8e55387ez4768z4ad9zbf5dz466e57ccb6f4
Quasi-Local 3D Quantum Gravity : Exact Amplitude and Holography
Goeller, C. (2019) · theses.fr (ABES) · doi:10.70675/c2eb659fz526ez4fd3za3b6z13d9e64178ac · Cited by 6
Towards quantum gravity as a field theory of discrete geometries
Laudonio, M. (2022) · theses.fr (ABES) · doi:10.70675/ec82bb75z7cbfz4319zb938zaad55e6ad953
Metadata
- Authors
- BOULATOV, D. V.
- Affiliations
- Commissariat à l'Énergie Atomique et aux Énergies Alternatives (FR)
- Corresponding author
- BOULATOV, D.V.
- Venue
- Modern Physics Letters A
- Publisher
- World Scientific Pub Co Pte Ltd
- Published
- 1992-06-14
- Volume
- 07
- Issue
- 18
- Pages
- 1629-1646
- ISSN
- 0217-7323 (ISSN-L)
- 1793-6632
- OpenAlex
- W2153297565
- Cited by
- 326
- References
- 3
- Citations by year
- 2026: 1 · 2025: 3 · 2024: 10 · 2023: 8 · 2022: 2 · 2021: 34 · 2020: 11 · 2019: 6 · 2018: 6 · 2017: 7 · 2016: 34 · 2015: 15 · 2014: 19 · 2013: 25 · 2012: 26
- FWCI
- 2.81
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Modern Physics Letters A (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Physics and Astronomy › Nuclear and High Energy 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
- simplicial quantum gravity, lattice gauge theory, Turaev-Viro invariants, Dijkgraaf-Witten theory, topological invariants, simplicial complexes, first cohomology group, Betti numbers, non-perturbative quantum gravity, three-dimensional gravity
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