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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.
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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
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)
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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
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