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Cited by 181Noncommutative and Quantum Gravity TheoriesRelativity and Gravitational TheoryBlack Holes and Theoretical Physics

Three-dimensional loop quantum gravity: physical scalar product and spin-foam models

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Noui, Karim, Perez, Alejandro·2005·Classical and Quantum Gravity
DOI 10.1088/0264-9381/22/9/017
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Abstract

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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Crossref · 10.1088/0264-9381/22/9/017

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49 of 49 references verified0 citation errors · 0 not checkable

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  • The Ponzano-Regge model is well defined when natural regularizations are used.

    “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]

  • The definition of the n-valent Barrett-Crane intertwiner is equivalent to that of [10-12].

    “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]

  • The cotangent bundle over SO(4) carries two different natural symplectic structures, related by a flip: one is obtained from the other by flipping the sign of the antiselfdual part.

    “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]

  • The possibility and relevance of a flipped symplectic structure was noticed by Baez and Barrett and by Montesinos.

    “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]

  • Montesinos has discussed the classical indeterminacy of the symplectic structure in detail.

    “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]

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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
DOI
10.1088/0264-9381/22/9/017
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
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 › Statistical and Nonlinear 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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