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Cited by 532Noncommutative and Quantum Gravity TheoriesRelativity and Gravitational TheoryBlack Holes and Theoretical Physics

Spin foam models for quantum gravity

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Perez, Alejandro·2003·Classical and Quantum Gravity
DOI 10.1088/0264-9381/20/6/202
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Abstract

In this topical review, we review the present status of the spin foam formulation of non-perturbative (background-independent) quantum gravity. The topical review is divided into two parts. In the first part, we present a general introduction to the main ideas emphasizing their motivation from various perspectives. Riemannian three-dimensional gravity is used as a simple example to illustrate conceptual issues and the main goals of the approach. The main features of the various existing models for four-dimensional gravity are also presented here. We conclude with a discussion of important questions to be addressed in four dimensions (gauge invariance, discretization independence, etc). In the second part, we concentrate on the definition of the Barrett–Crane model. We present the main results obtained in this framework from a critical perspective. Finally, we review the combinatorial formulation of spin foam models based on the dual group field theory technology. We present the Barrett–Crane model in this framework and review the finiteness results obtained for both its Riemannian and its Lorentzian variants.

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  • The Ponzano-Regge and Turaev-Viro models are examples of spin foam models, based on simplicial complexes with faces, edges, and vertices labeled by group representations and intertwiners.

    “The Ponzano-Regge and Turaev-Viro models are examples of “spin foam” models [35, 222], that is, a model based on simplicial complexes with faces, edges, and vertices labeled by group representations and intertwiners.”

    From Quantum Gravity in 2 + 1 Dimensions: The Case of a Closed Universe (2005) · cites this paper as [222]

  • The euclidean Barrett-Crane model may fail to yield the correct low-energy n-point functions.

    “Worse, recent calculations appear to indicate that some n -point functions fail to yield the correct low-energy limit [13].”

    From Loop-Quantum-Gravity Vertex Amplitude (2007) · cites this paper as [13]

  • The Barrett-Crane model was shown not to have sufficiently many degrees of freedom to ensure the correct classical limit.

    “Nonetheless, it was shown not to have sufficiently many degrees of freedom to ensure the correct classical limit [9].”

    From Spin-foams for all loop quantum gravity (2010) · cites this paper as [9]

  • The BC states are insufficient to define physical semi-classical states of quantum gravity.

    “A few years ago it was noticed [9], that the BC states are insufficient to define physical semi-classical states of quantum gravity.”

    From Spin-foams for all loop quantum gravity (2010) · cites this paper as [9]

  • The BC intertwiner space has 0 or 1 dimension per vertex.

    “The BC intertwiner space has 0 or 1 dimension per vertex and has been proven to insufficiently accommodate all the gravitational degrees of freedom.”

    From Spin-foams for all loop quantum gravity (2010) · cites this paper as [9]

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Authors
Perez, A.
Venue
Classical and Quantum Gravity
Publisher
IOP Publishing
Published
2003-02-21
Volume
20
Issue
6
Pages
R43-R104
ISSN
0264-9381 (ISSN-L)
DOI
10.1088/0264-9381/20/6/202
OpenAlex
W2125490099
Cited by
532
References
27
Citations by year
2026: 3 · 2025: 7 · 2024: 11 · 2023: 14 · 2022: 6 · 2021: 10 · 2020: 11 · 2019: 33 · 2018: 8 · 2017: 12 · 2016: 12 · 2015: 13 · 2014: 19 · 2013: 34 · 2012: 50
FWCI
22.67
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, quantum gravity, Barrett-Crane model, group field theory, background-independent quantum gravity, non-perturbative quantum gravity, four-dimensional gravity, gauge invariance

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