Semiclassical limits of extended Racah coefficients
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We explore the geometry and asymptotics of extended Racah coefficients. The extension is shown to have a simple relationship to the Racah coefficients for the positive discrete unitary representation series of SU(1,1) which is explicitly defined. Moreover, it is found that this extension may be geometrically identified with two types of Lorentzian tetrahedra for which all the faces are timelike. The asymptotic formulas derived for the extension are found to have a similar form to the standard Ponzano–Regge asymptotic formulas for the SU(2) 6j symbol and so should be viable for use in a state sum for three dimensional Lorentzian quantum gravity.
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It has been known for several years how to generalize the Ponzano-Regge action for a single tetrahedron, and recently considerable progress has been made in constructing Lorentzian spin foam models.
“It has been known for several years how to generalize the Ponzano-Regge action for a single tetrahedron [48, 101, 191], and recently considerable progress has been made in constructing Lorentzian spin foam models [222, 125, 102].”
From Quantum Gravity in 2 + 1 Dimensions: The Case of a Closed Universe (2005) · cites this paper as [101]
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- Authors
- Davids, S.
- Affiliations
- University of Nottingham (GB)
- Corresponding author
- Davids, Stefan
- Venue
- Journal of Mathematical Physics
- Publisher
- AIP Publishing
- Published
- 2000-02-01
- Volume
- 41
- Issue
- 2
- Pages
- 924-943
- ISSN
- 0022-2488 (ISSN-L)
- 1089-7658
- OpenAlex
- W2039509303
- Cited by
- 30
- References
- 0
- Citations by year
- 2025: 1 · 2024: 3 · 2023: 2 · 2021: 1 · 2020: 1 · 2018: 4 · 2013: 1
- FWCI
- 2.67
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Journal of Mathematical Physics (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 › Nuclear and High Energy Physics › Black Holes and Theoretical Physics
- Physical Sciences › Mathematics › Geometry and Topology › Geometric and Algebraic Topology
- Keywords
- semiclassical asymptotics, 6j symbols, Lorentzian quantum gravity, state sums, three-dimensional gravity
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