The DOI matches its Crossref record; 49 of the 49 references it cites were found in a registry or an index.
Three-dimensional loop quantum gravity: physical scalar product and spin-foam models
Open accessAbstract
In this paper, we address the problem of the dynamics in three-dimensional loop quantum gravity with zero cosmological constant. We construct a rigorous definition of Rovelli's generalized projection operator from the kinematical Hilbert space—corresponding to the quantization of the infinite-dimensional kinematical configuration space of the theory—to the physical Hilbert space. In particular, we provide the definition of the physical scalar product which can be represented in terms of a sum over (finite) spin-foam amplitudes. Therefore, we establish a clear-cut connection between the canonical quantization of three-dimensional gravity and spin-foam models. We emphasize two main properties of the result: first that no cut-off in the kinematical degrees of freedom of the theory is introduced (in contrast to standard ‘lattice’ methods), and second that no ill-defined sum over spins (‘bubble’ divergences) are present in the spin-foam representation.
Overview
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
In the citing paper
“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 [281]
In the citing paper
“That definition is merely equivalent to that of [10-12], however we spell it out in our notation for the clarity and the sake of precision.”
From Spin-foams for all loop quantum gravity (2010) · cites this paper as [11]
In the citing paper
“As pointed out in [29] and in [26], because of its peculiar SU (2) × SU (2) structure, the cotangent bundle over SO (4) carries indeed two different natural symplectic structures, related to one another by what Baez and Barrett call a fl ip : one is obtained from the other by flipping the sign of the antiselfdual part.”
From Flipped spinfoam vertex and loop gravity (2008) · cites this paper as [29]
In the citing paper
“The possibility and the relevance of a 'flipped' symplectic structure was noticed by Baez and Barrett in [26] (where they attribute the observation to Jos´ e-Antonio Zapata) and by Montesinos [29].”
From Flipped spinfoam vertex and loop gravity (2008) · cites this paper as [29]
In the citing paper
“Montesinos, in particular, has discussed the classical indeterminacy of the symplectic structure in detail.”
From Flipped spinfoam vertex and loop gravity (2008) · cites this paper as [29]
Citations
Cites
Kiefer, C. (2004) · Cited by 2,981
Rovelli, C. (2004) · doi:10.1017/cbo9780511755804 · Cited by 2,240
Modern Canonical Quantum General Relativity
Thiemann, T. (2007) · doi:10.1017/cbo9780511755682 · Cited by 2,001
Background independent quantum gravity: a status report
Ashtekar, A., & Lewandowski, J. (2004) · Classical and Quantum Gravity · doi:10.1088/0264-9381/21/15/r01 · Cited by 1,951
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
Quantum Invariants of Knots and 3-Manifolds
Turaev, V. G. (2010) · De Gruyter eBooks · doi:10.1515/9783110221848 · Cited by 923
(1998) · doi:10.12942/lrr-1998-1 · Cited by 917
Quantum Invariants of Knots and 3-Manifolds
Turaev, V. G. (1994) · doi:10.1515/9783110883275 · Cited by 832
Loop space representation of quantum general relativity
Rovelli, C., & Smolin, L. (1990) · Nuclear Physics B · doi:10.1016/0550-3213(90)90019-a · Cited by 806
Thiemann, T. (1998) · Classical and Quantum Gravity · doi:10.1088/0264-9381/15/4/011 · Cited by 750
Quantum Gravity in 2+1 Dimensions
Carlip, S. (1998) · doi:10.1017/cbo9780511564192 · Cited by 560
Spin foam models for quantum gravity
Perez, A. (2003) · Classical and Quantum Gravity · doi:10.1088/0264-9381/20/6/202 · Cited by 532
Quantization of diffeomorphism invariant theories of connections with local degrees of freedom
Ashtekar, A., Lewandowski, J., Marolf, D., Mourão, J., & Thiemann, T. (1995) · Journal of Mathematical Physics · doi:10.1063/1.531252 · Cited by 528
An Introduction to Spin Foam Models of BF Theory and Quantum Gravity
Baez, J. C. (2000) · Lecture Notes in Physics · doi:10.1007/3-540-46552-9_2 · Cited by 464
(1995) · CERN Document Server (European Organization for Nuclear Research) · Cited by 412
Lectures on Loop Quantum Gravity
Thiemann, T. (2003) · Lecture notes in physics · doi:10.1007/978-3-540-45230-0_3 · Cited by 390
Projective techniques and functional integration for gauge theories
Ashtekar, A., & Lewandowski, J. (1995) · Journal of Mathematical Physics · doi:10.1063/1.531037 · Cited by 388
Baez, J. C. (1998) · Classical and Quantum Gravity · doi:10.1088/0264-9381/15/7/004 · Cited by 381
TOPOLOGICAL LATTICE MODELS IN FOUR DIMENSIONS
OOGURI, H. (1992) · Modern Physics Letters A · doi:10.1142/s0217732392004171 · Cited by 379
Lectures on Loop Quantum GravityPreprint
Thiemann, T. (2003) · Cited by 286
Anomaly-free formulation of non-perturbative, four-dimensional Lorentzian quantum gravity
Thiemann, T. (1996) · Physics Letters B · doi:10.1016/0370-2693(96)00532-1 · Cited by 284
Nonperturbative quantum geometries
Jacobson, T., & Smolin, L. (1988) · Nuclear Physics B · doi:10.1016/0550-3213(88)90286-6 · Cited by 283
The Phoenix Project: master constraint programme for loop quantum gravity
Thiemann, T. (2006) · Classical and Quantum Gravity · doi:10.1088/0264-9381/23/7/002 · Cited by 272
Anomaly-free formulation of non-perturbative, four-dimensional Lorentzian quantum gravity
Thiemann, T. (1996) · Cited by 228
Combinatorial quantization of the Hamiltonian Chern-Simons theory I
Alekseev, A. Y., Grosse, H., & Schomerus, V. (1995) · Communications in Mathematical Physics · doi:10.1007/bf02099431 · Cited by 176
2+1 quantum gravity as a toy model for the 3+1 theory
Ashtekar, A., Husain, V, Rovelli, C., Samuel, J., & Smolin, L. (1989) · Classical and Quantum Gravity · doi:10.1088/0264-9381/6/10/001 · Cited by 165
Diffeomorphisms and spin foam models
Freidel, L., & Louapre, D. (2003) · Nuclear Physics B · doi:10.1016/s0550-3213(03)00306-7 · Cited by 155
Basis of the Ponzano-Regge-Turaev-Viro-Ooguri quantum-gravity model is the loop representation basis
Rovelli, C. (1993) · Physical Review D · doi:10.1103/physrevd.48.2702 · Cited by 140
Thiemann, T. (1998) · Classical and Quantum Gravity · doi:10.1088/0264-9381/15/5/011 · Cited by 128
Hamiltonian quantization of Chern Simons theory with SL (2, ) group
Buffenoir, E., Noui, K., & Roche, P. (2002) · Classical and Quantum Gravity · doi:10.1088/0264-9381/19/19/313 · Cited by 97
Self-citationProjector on physical states in loop quantum gravity
Rovelli, C. (1999) · Physical Review D · doi:10.1103/physrevd.59.104015 · Cited by 95
Spectra of length and area in (2 1) Lorentzian loop quantum gravity
Freidel, L., Livine, E. R., & Rovelli, C. (2003) · Classical and Quantum Gravity · doi:10.1088/0264-9381/20/8/304 · Cited by 93
A left-handed simplicial action for Euclidean general relativity
Reisenberger, M. P. (1997) · Classical and Quantum Gravity · doi:10.1088/0264-9381/14/7/012 · Cited by 73
Spin Foam Quantization and AnomaliesPreprint
Martin Bojowald, A., & Pérez, A. (2003) · Cited by 56
Three dimensional loop quantum gravity: coupling to point particles
Noui, K., & Pérez, A. (2004) · CERN Document Server (European Organization for Nuclear Research) · Cited by 54
Self-citationSpin foam diagrammatics and topological invariance
Girelli, F., Oeckl, R., & Perez, A. (2002) · Classical and Quantum Gravity · doi:10.1088/0264-9381/19/6/305 · Cited by 39
2D manifold-independent spinfoam theory
Livine, E. R., Pérez, A., & Carlo Rovelli, C. (2003) · Classical and Quantum Gravity · doi:10.1088/0264-9381/20/20/308 · Cited by 35
Generalized lattice gauge theory, spin foams and state sum invariants
Oeckl, R. (2003) · Journal of Geometry and Physics · doi:10.1016/s0393-0440(02)00148-1 · Cited by 33
Group Averaging and Refined Algebraic Quantization: Where are we now?Preprint
Marolf, D. M. (2000) · arXiv (Cornell University) · doi:10.48550/arxiv.gr-qc/0011112 · Cited by 32
Group averaging and refined algebraic quantization
Giulini, D. (2000) · Nuclear Physics B - Proceedings Supplements · doi:10.1016/s0920-5632(00)00808-2 · Cited by 27
Continuum spin foam model for 3d gravity
Zapata, J. A. (2002) · Journal of Mathematical Physics · doi:10.1063/1.1509850 · Cited by 24
Relating covariant and canonical approaches to triangulated models of quantum gravity
Arnsdorf, M. (2002) · Classical and Quantum Gravity · doi:10.1088/0264-9381/19/6/304 · Cited by 17
Canonical ``Loop'' Quantum Gravity and Spin Foam ModelsPreprint
Pietri, R. D. (1999) · arXiv (Cornell University) · doi:10.48550/arxiv.gr-qc/9903076 · Cited by 14
Flat spacetime vacuum in loop quantum gravity
Mikovi, A. (2004) · Classical and Quantum Gravity · doi:10.1088/0264-9381/21/16/006 · Cited by 12
Flat spacetime vacuum in loop quantum gravity
Miković, A. R. (2006) · Classical and Quantum Gravity · doi:10.1088/0264-9381/23/17/c01 · Cited by 10
The Status of Diffeomorphism Superselection in Euclidean 2+1 GravityPreprint
Marolf, D., Mourão, J., & Thiemann, T. (1997) · Cited by 10
Flat Spacetime Vacuum in Loop Quantum GravityPreprint
Miković, A. R. (2004) · arXiv (Cornell University) · doi:10.48550/arxiv.gr-qc/0404021 · Cited by 10
The status of diffeomorphism superselection in Euclidean 2+1 gravity
Marolf, D. M., Mourão, J., & Thiemann, T. (1997) · Journal of Mathematical Physics · doi:10.1063/1.532118 · Cited by 6
Canonical “Loop” Quantum Gravity and Spin Foam Models
Pietri, R. D. (2000) · Springer eBooks · doi:10.1007/978-88-470-2113-6_6 · Cited by 5
Research works printed but not linked: 2
- Rovelli C, 1998, Liv. Rev. Gen. Rel., 1, 1998
- Marolf D, 2000, Proc. M Grossmann Meeting on Recent Developments in Theoretical and Experimental General Relativity, Gravitation and Relativistic Field Theories (MG9)
Cited by
Sorted by citations
Background independent quantum gravity: a status report
Ashtekar, A., & Lewandowski, J. (2004) · Classical and Quantum Gravity · doi:10.1088/0264-9381/21/15/r01 · Cited by 1,951
The Spin-Foam Approach to Quantum Gravity
Perez, A. (2013) · Living Reviews in Relativity · doi:10.12942/lrr-2013-3 · Cited by 677
LQG vertex with finite Immirzi parameter
Engle, J., Livine, E., Pereira, R., & Rovelli, C. (2008) · Nuclear Physics B · doi:10.1016/j.nuclphysb.2008.02.018 · Cited by 584
Group Field Theory: An Overview
Freidel, L. (2005) · International Journal of Theoretical Physics · doi:10.1007/s10773-005-8894-1 · Cited by 378
Loop-Quantum-Gravity Vertex Amplitude
Engle, J., Pereira, R., & Rovelli, C. (2007) · Physical Review Letters · doi:10.1103/physrevlett.99.161301 · Cited by 335
Metadata
- Authors
- Noui, K., & Perez, A.
- Affiliations
- Pennsylvania State University (US)
- ORCID
- Noui, Karim
- Venue
- Classical and Quantum Gravity
- Publisher
- IOP Publishing
- Published
- 2005-04-12
- Volume
- 22
- Issue
- 9
- Pages
- 1739-1761
- ISSN
- 0264-9381 (ISSN-L)
- 1361-6382
- OpenAlex
- W1978695735
- Cited by
- 181
- References
- 49
- Citations by year
- 2026: 1 · 2025: 1 · 2024: 4 · 2023: 4 · 2022: 2 · 2021: 3 · 2020: 4 · 2019: 6 · 2018: 6 · 2017: 2 · 2016: 7 · 2015: 10 · 2014: 13 · 2013: 15 · 2012: 21
- FWCI
- 8.42
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Classical and Quantum Gravity (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 › Physics and Astronomy › Astronomy and Astrophysics › Relativity and Gravitational Theory
- Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Black Holes and Theoretical Physics
- Keywords
- spin foam models, physical Hilbert space, canonical quantization of gravity, zero cosmological constant, kinematical Hilbert space
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 ›
Are you an author, or do you see a problem with this page? Request a review
