Partition functions and topology-changing amplitudes in the three-dimensional lattice gravity of Ponzano and Regge
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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 [219]
The Introduction (p. 5) describes the Ponzano–Regge model as the k → ∞ limit relevant to the Turaev–Viro conjecture, and Wave-Functions (p. 11) establishes an isomorphism of physical Hilbert spaces. But Wave-Functions (p. 8) identifies the corresponding states as half-densities on the moduli space of flat SO(3) connections, not simply gauge-invariant functions of flat SU(2) connections. (LLM, conf=0.88)
Experimental — accuracy not yet measuredThe OCY model is a 4d generalization of the Ponzano-Regge-Turaev-Viro (PRTV) model.
“The OCY model is a 4d generalization of the Ponzano-Regge-Turaev-Viro (PRTV) model [12,13], which, in turn, can be seen as a quantization of 3d GR, or a quantization of 3d Chern-Simon theory.”
From “Sum over surfaces” form of loop quantum gravity (1997) · cites this paper as [12]
The PRTV model can be seen as a quantization of 3d GR, or a quantization of 3d Chern-Simon theory.
“The OCY model is a 4d generalization of the Ponzano-Regge-Turaev-Viro (PRTV) model [12,13], which, in turn, can be seen as a quantization of 3d GR, or a quantization of 3d Chern-Simon theory.”
From “Sum over surfaces” form of loop quantum gravity (1997) · cites this paper as [12]
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Basis of the Ponzano-Regge-Turaev-Viro-Ooguri quantum-gravity model is the loop representation basis
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“It is now known that the Ponzano-Regge model is equivalent to a ChernSimons-Witten model with gauge group ISO(3) [316, 317] and can also be transformed to a loop representation [318].”
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“[61] H.”
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“Like (5), this expression needs gauge-fixing, as was realized already by Ponzano and Regge (see also [42]).”
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“Starting with the Ponzano–Regge model [28, 29], a progression through models defined in a variety of simplified settings [30–33] culminated within the framework of LQG to what has become known as the EPRL model [34–40], that treats the physically pertinent Lorentzian case.”
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“this is done by constructing the generalised projector. In contrast to the previous section one can give an exact expression of this projector in terms of sums over triangulations. As shown by Ooguri [16], the Ponzano-Regge model defines the projector for 2+1 quantum gravity. This is most easily introduced in terms of…”
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4-dimensional BF gravity on the lattice
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“owing state sum ZPR(M;4;fj@4g) = X fj4g Y ˙1 ( 1)2jd j Y ˙3 ( 1) P6 i=1 ji n j1 2 5 j3 j4 j6 o : (3.55) The path integral Z PR acts as a projector on a spin network state by performing its evaluation [50,51]. More precisely, in the case where the manifold Mhas boundaries, if we think of the components of @4as dual to…”
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BTZ BLACK HOLE ENTROPY FROM PONZANO–REGGE GRAVITY
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“Turaev-Viro partition function denes quantised gravity in three dimensions given by the action (7.1). The equivalence of the Turaev-Viro model with 3D quantum gravity was demonstrated explicitly in [47] by showing that the Hilbert space of states of the Turaev-Viro model in the k!1limit, which is the Ponzano-Regge mod…”
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“The Ponzano-Regge model and its quantum group analogous, the Turaev-Viro partition function [it is known that its evaluation gives a quantum invariants of 3-manifolds], are the better understood example of theory formulated on a triangulation � of a manifold M. From the physical point of view it is known (for details…”
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“Essentially GFT is a QFT on superspace1 (space of 3 geometries), which is defined utilising simplicial description of spacetime, thus rendering the theory local2.”
BackgroundInfluentialSpinfoam Models for Quantum Gravity
Livine, E. R. (2024) · Encyclopedia of Mathematical Physics · doi:10.1016/b978-0-323-95703-8.00253-6 · Cited by 8 · see citing works
“…of this path integral are: • it defines a projector on physical states, given by the moduli space of flat connections, as expected for BF theory [67]; • it is topologically-invariant, in the sense that it des not depend on the details of the bulk triangulation but only on its overall topology;…”
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Canonical “Loop” Quantum Gravity and Spin Foam Models
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“The Ponzano-Regge model and its quantum group analogous, the Turaev-Viro partition function [it is known that its evaluation gives a quantum invariants of 3-manifolds], are the better understood example of theory formulated on a triangulation � of a manifold M. From the physical point of view it is known (for details…”
MethodInfluentialConditional probabilities in Ponzano-Regge minisuperspace
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12j-symbols and four-dimensional quantum gravity
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“To do so, we will first show that the Ponzano-Regge model can be seen as a projector [166, 70, 73] into the physical Hilbert space construct from standard loop quantum gravity technique.”
3D quantum gravity from holomorphic blocks
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Quantum Gravity in 2+1 Dimensions
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“To do so, we will first show that the Ponzano-Regge model can be seen as a projector [166, 70, 73] into the physical Hilbert space construct from standard loop quantum gravity technique.”
- Authors
- Ooguri, H.
- Affiliations
- Kyoto University (JP)
- Corresponding author
- Ooguri, Hirosi
- ORCID
- Ooguri, Hirosi
- Venue
- Nuclear Physics B
- Publisher
- Elsevier BV
- Published
- 1992-09
- Volume
- 382
- Issue
- 2
- Pages
- 276-304
- ISSN
- 0550-3213 (ISSN-L)
- OpenAlex
- W2952120209
- Cited by
- 76
- References
- 17
- Citations by year
- 2026: 1 · 2024: 3 · 2023: 1 · 2021: 2 · 2020: 1 · 2019: 1 · 2018: 2 · 2015: 1 · 2014: 1 · 2013: 1 · 2012: 3
- FWCI
- 3.93
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Nuclear Physics B (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- Institutional Repositories DataBase (IRDB) (submittedVersion)
- CaltechAUTHORS (California Institute of Technology) (submittedVersion)
- Kyoto University Research Information Repository (Kyoto University) (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
- Ponzano-Regge model, lattice gravity, physical Hilbert space, Hartle-Hawking wave function, handlebodies, Heegaard splittings, partition function, quantum gravity, 3-manifolds
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
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