Asymptotics of 6 j and 10 j symbols
Open accessAbstract
It is well known that the building blocks for state sum models of quantum gravity are given by 6 j and 10 j symbols. In this work, we study the asymptotics of these symbols by using their expressions as group integrals. We carefully describe the measure involved in terms of invariant variables and develop new technics in order to study their asymptotics. Using these technics, we compute the asymptotics of the various Euclidean and Lorentzian 6 j symbols. Finally, we compute the asymptotic expansion of the 10 j symbol which is shown to be non-oscillating, in agreement with a recent result of Baez et al . We discuss the physical origin of this behaviour and a way to modify the Barrett–Crane model in order to cure this disease.
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The physical state selects the 'forward' propagating component of the transition amplitude.
“Thus, the physical state selects the 'forward' propagating [22] component of the transition amplitude.”
From Graviton Propagator from Background-Independent Quantum Gravity (2006) · cites this paper as [22]
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References 14 · Cited by 113
Research works printed but not linked: 7
- Baez J C, Christensen J D and Egan G 2002 Asymptotics of 10J symbols Preprint gr-qc/0208010 · arXiv
- Barrett J W and Steele C M 2002 Asymptotics of relativistic spin networks Preprint gr-qc/0209023 · arXiv
- Alekseevskij D V, Vinberg E B and Solodovnikov A S 1993 Geometry of Spaces of Constant (Curvature Encyclopaedia of Mathematical Sciences vol 29) (Berlin: Springer)
- Barrett J W 2002 Geometrical measurements in three-dimensional quantum gravity Preprint gr-qc/0203018 · arXiv
- Knapp A W 1986 Representation of Semi-Simple Groups (Princeton, NJ: Princeton University Press)
- Freidel L and Livine E R 2002 Spin networks for non-compact groups Preprint hep-th/0205268 · arXiv
- Reisenberger M 1998 Classical Euclidean general relativity from 'left-handed area = right-handed area' Preprint gr-qc/9804061 · arXiv
- Authors
- Freidel, L., & Louapre, D.
- Affiliations
- École Normale Supérieure de Lyon (FR)
- Venue
- Classical and Quantum Gravity
- Publisher
- IOP Publishing
- Published
- 2003-03-10
- Volume
- 20
- Issue
- 7
- Pages
- 1267-1294
- ISSN
- 0264-9381 (ISSN-L)
- OpenAlex
- W1533199519
- Cited by
- 113
- References
- 14
- Citations by year
- 2026: 1 · 2025: 1 · 2024: 1 · 2023: 1 · 2022: 4 · 2021: 2 · 2020: 2 · 2019: 1 · 2018: 3 · 2017: 1 · 2016: 2 · 2015: 4 · 2014: 5 · 2013: 10 · 2012: 4
- Type
- other
- Language
- he
- Open access
- bronze
- doi.org
- Locations
- Classical and Quantum Gravity (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- arXiv (Cornell University)
- Funders
- Centre National de la Recherche Scientifique
- 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
- 6j symbols, asymptotic expansion, group integrals, invariant variables, state sum models, quantum gravity, Barrett-Crane model
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