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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.
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“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]
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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
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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
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