The DOI matches its Crossref record; 39 of the 39 references it cites were found in a registry or an index.
On the regularization of the constraint algebra of quantum gravity in 2 + 1 dimensions with a nonvanishing cosmological constant
Open accessAbstract
We use the mathematical framework of loop quantum gravity (LQG) to study the quantization of three-dimensional (Riemannian) gravity with a positive cosmological constant (Λ > 0). We show that the usual regularization techniques (successful in the Λ = 0 case and widely applied in four-dimensional LQG) led to a deformation of the classical constraint algebra (or anomaly) proportional to the local strength of the curvature squared. We argue that this is an unavoidable consequence of the nonlocal nature of generalized connections.
Overview
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
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
“In the simple case of 3D gravity with cosmological constant, this can be shown explicitly at the classical level [45] as well as at the quantum level [304].”
From The Spin-Foam Approach to Quantum Gravity (2013) · cites this paper as [304]
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Citations
Cites
Quantum field theory and the Jones polynomial
Witten, E. (1989) · Communications in Mathematical Physics · doi:10.1007/bf01217730 · Cited by 4,758
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
Modern Canonical Quantum General Relativity
Thiemann, T. (2007) · doi:10.1017/cbo9780511755682 · Cited by 2,001
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
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
SEMICLASSICAL LIMIT OF RACAH COEFFICIENTS.
Ponzano, G., & Regge, T. (1969) · OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information) · Cited by 353
Uniqueness of Diffeomorphism Invariant States on Holonomy–Flux Algebras
Lewandowski, J., Okołów, A., Sahlmann, H., & Thiemann, T. (2006) · Communications in Mathematical Physics · doi:10.1007/s00220-006-0100-7 · Cited by 297
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
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
Poisson structure on moduli of flat connections on Riemann surfaces and the 𝑟-matrix
Fock, V. V., & Rosly, A. A. (1999) · Translations - American Mathematical Society/Translations · doi:10.1090/trans2/191/03 · Cited by 206
Cited by
Sorted by citations
The Spin-Foam Approach to Quantum Gravity
Perez, A. (2013) · Living Reviews in Relativity · doi:10.12942/lrr-2013-3 · Cited by 677
Bojowald, M. (2015) · Reports on Progress in Physics · doi:10.1088/0034-4885/78/2/023901 · Cited by 174
Deformed general relativity and effective actions from loop quantum gravity
Martin Bojowald, A., & Paily, G. M. (2012) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.86.104018 · Cited by 149
Covariance in models of loop quantum gravity: Spherical symmetry
Martin Bojowald, A., Brahma, S., & Reyes, J. D. (2015) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.92.045043 · Cited by 107
Anomaly-free cosmological perturbations in effective canonical quantum gravity
Barrau, A., Martin Bojowald, A., Calcagni, G., Grain, J., & Kagan, M. (2015) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2015/05/051 · Cited by 120
Coarse graining methods for spin net and spin foam models
Dittrich, B., Eckert, F. C., & Martín-Benito, M. (2012) · New Journal of Physics · doi:10.1088/1367-2630/14/3/035008 · Cited by 103
Some implications of signature-change in cosmological models of loop quantum gravity
Martin Bojowald, A., & B, J. M. A. (2015) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2015/08/052 · Cited by 91
Spin Foams and Canonical Quantization
Alexandrov, S. Y. (2012) · Symmetry Integrability and Geometry Methods and Applications · doi:10.3842/sigma.2012.055 · Cited by 101
Cosmological constant in spinfoam cosmology
Eugenio Bianchi, A., Krajewski, T., Carlo Rovelli, C., & Vidotto, F. (2011) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.83.104015 · Cited by 62
Black-Hole Models in Loop Quantum Gravity
Martin Bojowald, A. (2020) · Universe · doi:10.3390/universe6080125 · Cited by 70
2 Quantum Cosmology: Effective TheoryPreprint
Martin Bojowald, A. (2016) · Cited by 66
Hypersurface-deformation algebroids and effective spacetime models
Martin Bojowald, A., Büyükçam, U., Brahma, S., & D’Ambrosio, F. (2016) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.94.104032 · Cited by 57
Martin Bojowald, A., & Paily, G. M. (2013) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.87.044044 · Cited by 62
Canonical quantization of non-commutative holonomies in 2 + 1 loop quantum gravity
Noui, K., Perez, A., & Pranzetti, D. (2011) · Journal of High Energy Physics · doi:10.1007/jhep10(2011)036 · Cited by 56
Self-citationConstraint algebra in loop quantum gravity reloaded. I. Toy model of a U(1)3 gauge theory
Henderson, A., Laddha, A., & Tomlin, C. (2013) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.88.044028 · Cited by 50
The Hilbert space of 3d gravity: quantum group symmetries and observables
Meusburger, C., & Noui, K. (2010) · Advances in Theoretical and Mathematical Physics · doi:10.4310/atmp.2010.v14.n6.a3 · Cited by 58
Spacetime-noncommutativity regime of loop quantum gravity
Giovanni Amelino-camelia, A., Silva, M. M. D., Ronco, M., Cesarini, L., & Lecian, O. M. (2017) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.95.024028 · Cited by 47
Symmetries of quantum spacetime in three dimensions
Cianfrani, F., Kowalski-Glikman, J., Pranzetti, D., & Rosati, G. (2016) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.94.084044 · Cited by 55
Self-citationStatistical entropy of a BTZ black hole from loop quantum gravity
Frodden, E., Geiller, M., Noui, K., & Pérez, A. (2013) · Journal of High Energy Physics · doi:10.1007/jhep05(2013)139 · Cited by 44
Discreteness corrections and higher spatial derivatives in effective canonical quantum gravity
Martin Bojowald, A., Paily, G. M., & Reyes, J. D. (2014) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.90.025025 · Cited by 40
Information loss, made worse by quantum gravity?
Martin Bojowald, A. (2015) · Frontiers in Physics · doi:10.3389/fphy.2015.00033 · Cited by 40
Mathematical Structure of Loop Quantum Cosmology: Homogeneous Models
Martin Bojowald, A. (2013) · Symmetry Integrability and Geometry Methods and Applications · doi:10.3842/sigma.2013.082 · Cited by 38
Turaev-Viro amplitudes from 2+1 loop quantum gravity
Pranzetti, D. (2014) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.89.084058 · Cited by 45
Self-citationHorizon entropy with loop quantum gravity methods
Pranzetti, D., & Sahlmann, H. (2015) · Physics Letters B · doi:10.1016/j.physletb.2015.04.070 · Cited by 28
Self-citationNonlinear (loop) quantum cosmology
Martin Bojowald, A., Chinchilli, A. L., Simpson, D., Dantas, C. C., & Jaffe, M. (2012) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.86.124027 · Cited by 25
On the UV Dimensions of Loop Quantum Gravity
Ronco, M. (2016) · Advances in High Energy Physics · doi:10.1155/2016/9897051 · Cited by 19
Effective Field Theory of Loop Quantum Cosmology
Martin Bojowald, A. (2019) · Universe · doi:10.3390/universe5020044 · Cited by 17
Anomaly freedom in perturbative models of Euclidean loop quantum gravity
Wu, J.-P., Martin Bojowald, A., & Ma, Y. (2018) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.98.106009 · Cited by 18
Non-commutative holonomies in 2 + 1 LQG and Kauffman's brackets
Noui, K., Pérez, A., & Pranzetti, D. (2012) · Journal of Physics Conference Series · doi:10.1088/1742-6596/360/1/012040 · Cited by 18
Self-citationA no-singularity scenario in loop quantum gravity
Martin Bojowald, A., & Paily, G. M. (2012) · Classical and Quantum Gravity · doi:10.1088/0264-9381/29/24/242002 · Cited by 20
Effective constraint algebras with structure functions
Martin Bojowald, A., & Brahma, S. (2016) · Journal of Physics A Mathematical and Theoretical · doi:10.1088/1751-8113/49/12/125301 · Cited by 18
Lessons for Loop Quantum Gravity from Parametrised Field TheoryPreprint
Thiemann, T. (2010) · arXiv (Cornell University) · doi:10.48550/arxiv.1010.2426 · Cited by 18
Constraining the loop quantum gravity parameter space from phenomenology
Brahma, S., & Ronco, M. (2018) · Physics Letters B · doi:10.1016/j.physletb.2018.01.023 · Cited by 14
Escalante, A., & Rodríguez-Tzompantzi, O. (2014) · Journal of High Energy Physics · doi:10.1007/jhep05(2014)073 · Cited by 13
Lessons from Toy-Models for the Dynamics of Loop Quantum Gravity
Bonzom, V. (2012) · Symmetry Integrability and Geometry Methods and Applications · doi:10.3842/sigma.2012.009 · Cited by 15
Martin Bojowald, A. (2013) · AIP conference proceedings · doi:10.1063/1.4791718 · Cited by 14
Engle, J., & Simone Speziale, D. (2023) · Springer eBooks · doi:10.1007/978-981-19-3079-9_99-1 · Cited by 18
Cosmological Constant from Condensation of Defect Excitations
Dittrich, B. (2018) · Universe · doi:10.3390/universe4070081 · Cited by 13
Electric time in quantum cosmology
Alexander, S., Martin Bojowald, A., Marcianò, A., & Simpson, D. (2013) · Classical and Quantum Gravity · doi:10.1088/0264-9381/30/15/155024 · Cited by 11
Extending general covariance: Moyal-type noncommutative manifolds
Martin Bojowald, A., Brahma, S., Büyükçam, U., & Ronco, M. (2018) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.98.026031 · Cited by 10
Inequivalence of mimetic gravity with models of loop quantum gravity
Martin Bojowald, A., & Duque, E. I. (2024) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.109.084044 · Cited by 9
Martin Bojowald, A., Brahma, S., Ding, D., & Ronco, M. (2020) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.101.026001 · Cited by 9
2 + 1 gravity with a positive cosmological constant in LQG: a proposal for the physical state
Pranzetti, D. (2011) · Classical and Quantum Gravity · doi:10.1088/0264-9381/28/22/225025 · Cited by 8
Self-citationQuantum Matter in Quantum Space-Time
Martin Bojowald, A., Hossain, G. M., Kagan, M. A., & Tomlin, C. (2013) · Quantum Matter · doi:10.1166/qm.2013.1078 · Cited by 6
Dynamical emergence of SUq(2) from the regularization of (2+1)D gravity with a cosmological constant
Gresnigt, N. G., Marcianò, A., & Zappala, E. (2023) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.107.046018 · Cited by 4
General gravitational Lagrangian with deformed covariance
Cuttell, R., & Sakellariadou, M. (2020) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.102.104048 · Cited by 4
Quantum gravity, space-time structure, and cosmology
Martin Bojowald, A. (2012) · Journal of Physics Conference Series · doi:10.1088/1742-6596/405/1/012001 · Cited by 2
Black-hole models in loop quantum gravityPreprint
Martin Bojowald, A. (2020) · arXiv (Cornell University) · doi:10.48550/arxiv.2009.13565 · Cited by 2
Engle, J., & Simone Speziale, D. (2024) · Springer eBooks · doi:10.1007/978-981-99-7681-2_99 · Cited by 1
Quantum gravity effects on space-timePreprint
Martin Bojowald, A. (2010) · arXiv (Cornell University) · doi:10.48550/arxiv.1002.2618 · Cited by 5
Calcagni, G. (2017) · Graduate texts in physics · doi:10.1007/978-3-319-41127-9_10
TQFT and Loop Quantum Gravity : 2+1 Theory and Black Hole Entropy
Pranzetti, D. (2011) · theses.fr (ABES) · doi:10.70675/51f92df4zd74bz44c9z95eazf924851241ec
Self-citationLoop Quantum Cosmology, Space-Time Structure, and Falsifiability
Martin Bojowald, A. (2012) · Lecture notes in physics · doi:10.1007/978-3-642-33036-0_7
Metadata
- Authors
- Perez, A., & Pranzetti, D.
- Affiliations
- Centre de Physique Théorique (FR)
- ORCID
- Pranzetti, Daniele
- Venue
- Classical and Quantum Gravity
- Publisher
- IOP Publishing
- Published
- 2010-05-28
- Volume
- 27
- Issue
- 14
- Pages
- 145009
- ISSN
- 0264-9381 (ISSN-L)
- 1361-6382
- OpenAlex
- W2168468091
- Cited by
- 53
- References
- 39
- Citations by year
- 2024: 2 · 2023: 2 · 2020: 4 · 2019: 1 · 2018: 4 · 2017: 2 · 2016: 5 · 2015: 6 · 2014: 3 · 2013: 8 · 2012: 9
- FWCI
- 5.44
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Classical and Quantum Gravity (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- HAL (submittedVersion)
- HAL (submittedVersion, other-oa)
- SDL (submittedVersion)
- Trinity's Access to Research Output (TARA) (Trinity College Dublin) (submittedVersion)
- arXiv (Cornell University)
- Funders
- Agence Nationale de la Recherche (ANR-06-BLAN-0050)
- Institut Universitaire de France
- 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
- loop quantum gravity, three-dimensional gravity, positive cosmological constant, constraint algebra, regularization, anomalies, generalized connections, nonlocality
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
