The DOI matches its Crossref record; 7 of the 8 references it cites were found in a registry or an index.
TOPOLOGICAL LATTICE MODELS IN FOUR DIMENSIONS
Open accessAbstract
We define a lattice statistical model on a triangulated manifold in four dimensions associated to a group G. When G= SU (2), the statistical weight is constructed from the 15j-symbol as well as the 6j-symbol for recombination of angular momenta, and the model may be regarded as the four-dimensional version of the Ponzano-Regge model. We show that the partition function of the model is invariant under the Alexander moves of the simplicial complex, thus it depends only on the piecewise linear topology of the manifold. For an orientable manifold, the model is related to the so-called BF model. The q-analog of the model is also constructed, and it is argued that its partition function is invariant under the Alexander moves. It is discussed how to realize the 't Hooft operator in these models associated to a closed surface in four dimensions as well as the Wilson operator associated to a closed loop. Correlation functions of these operators in the q-deformed version of the model would define a new type of invariants of knots and links in four dimensions.
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“More specifically, our expression for the proper time propagator U ( T ) of GR as a sum over worldsheets resembles in many ways the worldsheet sum [8,56] 14 for the projector on physical states, U OCY , of the OCY model.”
From “Sum over surfaces” form of loop quantum gravity (1997) · cites this paper as [8]
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“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 [8]
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“There is a natural way of interpreting a branched colored surface σ as a discrete ('quantum') geometry. This geometrical interpretation was proposed in [8] in a slightly different context; it holds in the worldsheet formulation of the simplicial model of GR [9].”
From “Sum over surfaces” form of loop quantum gravity (1997) · cites this paper as [8]
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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
Elementary Differential Topology.
Linton, F. E. J., & Munkres, J. R. (1966) · American Mathematical Monthly · doi:10.2307/2315380 · Cited by 477
Spectroscopic and Group Theoretical Methods in Physics
Blin-Stoyle, R. J. (1969) · Physics Bulletin · doi:10.1088/0031-9112/20/9/009 · Cited by 239
The Racah–Wigner Algebra in Quantum Theory
Biedenharn, L. C., & Louck, J. D. (1984) · Cambridge University Press eBooks · doi:10.1017/cbo9781107340695.006 · Cited by 217
Infinite Dimensional Lie Algebras and Groups
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Spectroscopic and Group Theoretical Methods in Physics
Bloch, F., Cohen, S. G., De-Shalit, A., Sambursky, S., & Talmi, I. (1968) · Cited by 162
ELEMENTARY DIFFERENTIAL TOPOLOGY
Cockcroft, W. H. (1964) · Journal of the London Mathematical Society · doi:10.1112/jlms/s1-39.1.380b · Cited by 81
Research works printed but not linked: 6
- [1][1] M.E. Agishtein and A.A. Migdal, Mod. Phys. Lett. A6 (1991) 1863; J. Ambjorn and S. Varsted, Phys. Lett. B226 (1991) 258; D.V. Boulatov and A. Krzywicki, Mod. Phys. Letts A6 (1991) 3005; J. Ambjorn, D. Boulatov, A. Krzywicki and S. Varsted, preprint NBI-HE-91-46 (1991). -
- [2][2] M.E. Agishtein and A.A. Migdal, preprint PUPT-1287 (1991), PUPT- (1992); J. Ambjorn and J. Jurkiewicz, preprint NBI-HE-91-47 (1991). -
- [5][5] D.V. Boulatov, preprint SPhT/92-017 (1992) -
- [7][7] M. Gross and S. Varsted, preprint NBI-HE-91-33 (1991) -
- [12][12] V.G. Turaev, C. R. Acad. Sci. Paris, t. 313, S´ erie I (1991) 395; K. Walker, ' On Witten's 3 -Manifold Invariants ,' preprint (1990). -
- [13][13] H. Ooguri and N. Sasakura, Mod. Phys. Lett. A6 (1991) 3591; H. Ooguri, preprint RIMS-851 (1991), to be published in Nucl. Phys. B . -
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Metadata
- Authors
- OOGURI, H.
- Affiliations
- Kyoto University (JP)
- Corresponding author
- OOGURI, HIROSI
- ORCID
- OOGURI, HIROSI
- Venue
- Modern Physics Letters A
- Publisher
- World Scientific Pub Co Pte Lt
- Published
- 1992-09-28
- Volume
- 07
- Issue
- 30
- Pages
- 2799-2810
- ISSN
- 0217-7323 (ISSN-L)
- 1793-6632
- OpenAlex
- W2171017579
- Cited by
- 379
- References
- 8
- Citations by year
- 2026: 2 · 2025: 1 · 2024: 10 · 2023: 55 · 2022: 5 · 2021: 5 · 2020: 4 · 2019: 9 · 2018: 5 · 2017: 5 · 2016: 29 · 2015: 11 · 2014: 15 · 2013: 24 · 2012: 29
- FWCI
- 9.01
- 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 › Mathematics › Geometry and Topology › Geometric and Algebraic Topology
- Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Noncommutative and Quantum Gravity Theories
- Physical Sciences › Mathematics › Geometry and Topology › Algebraic structures and combinatorial models
- Keywords
- triangulated manifolds, Ponzano-Regge model, 6j symbols, piecewise linear topology, BF model, q-deformation, Wilson loops, SU(2) gauge theory, four-dimensional quantum gravity
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