Semiclassical limits of simplicial quantum gravity
Open accessAbstract
We consider the simplicial state sum model of Ponzano and Regge as a path integral for quantum gravity in three dimensions. We examine the Lorentzian geometry of a single 3-simplex and of a simplicial manifold, and interpret an asymptotic formula for 6j-symbols in terms of this geometry. This extends Ponzano and Regge's similar interpretation for Euclidian geometry. We give a geometric interpretation of the stationary points of this state sum, by showing that, at these points, the simplicial manifold may be mapped locally into flat Lorentzian or Euclidian space. This lends weight to the interpretation of the state sum as a path integral, which has solutions corresponding to both Lorentzian and Euclidian gravity in three dimensions.
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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 [48]
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Ooguri, H. (1992) · Nuclear Physics B · doi:10.1016/0550-3213(92)90188-h · Cited by 76 · see citing works
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Research works printed but not linked: 1
- Tumev V G and Vir0 0 Y 1992 Shte sum invariants of 3-manifolds and quanNm 6 j symbols Topology 31 methods in physics ed P Bloch (Amsterdam North-Holland) ed T Bastin (Cambridge: Cambridge University Press)
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Lorentzian spin foam amplitudes: graphical calculus and asymptotics
Barrett, J. W., Dowdall, R. J., Fairbairn, W. J., Hellmann, F., & Pereira, R. (2010) · Classical and Quantum Gravity · doi:10.1088/0264-9381/27/16/165009 · Cited by 247 · see citing works
Self-citationQuantum Gravity in 2 + 1 Dimensions: The Case of a Closed Universe
Carlip, S. (2005) · Living Reviews in Relativity · doi:10.12942/lrr-2005-1 · Cited by 172 · see citing works
Barrett, J. W., & Naish-Guzman, I. (2009) · Classical and Quantum Gravity · doi:10.1088/0264-9381/26/15/155014 · Cited by 131 · see citing works
Self-citationBarrett, J. W. (1994) · Classical and Quantum Gravity · doi:10.1088/0264-9381/11/11/013 · Cited by 54 · see citing works
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- Authors
- Barrett, J. W., & Foxon, T. J.
- Affiliations
- University of Nottingham (GB)
- University of Cambridge (GB)
- ORCID
- Foxon, T J
- Venue
- Classical and Quantum Gravity
- Publisher
- IOP Publishing
- Published
- 1994-03-01
- Volume
- 11
- Issue
- 3
- Pages
- 543-556
- ISSN
- 0264-9381 (ISSN-L)
- 1361-6382
- OpenAlex
- W2005195651
- Cited by
- 65
- References
- 1
- Citations by year
- 2026: 1 · 2025: 1 · 2024: 6 · 2023: 2 · 2022: 1 · 2021: 2 · 2020: 3 · 2019: 4 · 2018: 5 · 2017: 2 · 2016: 2 · 2015: 1 · 2014: 1 · 2013: 5 · 2012: 4
- FWCI
- 2.21
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Classical and Quantum Gravity (publishedVersion)
- arXiv (Cornell University) (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
- simplicial quantum gravity, Ponzano-Regge model, semiclassical limit, 6j symbols, Lorentzian geometry, three-dimensional quantum gravity, path integral, state sum models
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