Asymptotic analysis of the Engle–Pereira–Rovelli–Livine four-simplex amplitude
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The semiclassical limit of a four-simplex amplitude for a spin foam quantum gravity model with an Immirzi parameter is studied. If the boundary state represents a nondegenerate four-simplex geometry, the asymptotic formula contains the Regge action for general relativity. A canonical choice of phase for the boundary state is introduced and is shown to be necessary to obtain the results.
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For Regge-like boundary data, the action (215) has exactly two critical points leading to the asymptotic formula.
“For such boundary data, the action (215) has exactly two critical points leading to the asymptotic formula 216”
From The Spin-Foam Approach to Quantum Gravity (2013) · cites this paper as [61]
On a fixed discretization, the semiclassical limit of the EPRL-FK models is given by Regge's discrete formulation of general relativity.
“we now present the results on the large-spin asymptotics of the spin-foam amplitudes suggesting that, on a fixed discretization, the semiclassical limit of the EPRL-FK models is given by Regge’s discrete formulation of general relativity [61, 64].”
From The Spin-Foam Approach to Quantum Gravity (2013) · cites this paper as [61]
The Riemannian EPRL vertex asymptotics is the unbalanced square of the SU(2) asymptotics, and the resulting asymptotic formula is also valid for γ > 1.
“implies the asymptotic formula for the vertex amplitude to be given by the unbalanced square of the above formula [62], namely One can write the previous expression as 217”
From The Spin-Foam Approach to Quantum Gravity (2013) · cites this paper as [61]
Non-geometric configurations are exponentially suppressed.
“Non-geometric configurations are exponentially suppressed.”
From The Spin-Foam Approach to Quantum Gravity (2013) · cites this paper as [61]
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- Authors
- Barrett, J. W., Dowdall, R. J., Fairbairn, W. J., Gomes, H., & Hellmann, F.
- Affiliations
- University of Nottingham (GB)
- Venue
- Journal of Mathematical Physics
- Publisher
- AIP Publishing
- Published
- 2009-11-01
- Volume
- 50
- Issue
- 11
- ISSN
- 0022-2488 (ISSN-L)
- 1089-7658
- OpenAlex
- W1916854187
- Cited by
- 224
- References
- 40
- Citations by year
- 2026: 3 · 2025: 3 · 2024: 11 · 2023: 10 · 2022: 6 · 2021: 11 · 2020: 12 · 2019: 12 · 2018: 21 · 2017: 9 · 2016: 15 · 2015: 3 · 2014: 10 · 2013: 26 · 2012: 20
- FWCI
- 16.52
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Journal of Mathematical Physics (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
- spin foam models, Immirzi parameter, semiclassical limit, asymptotic analysis, Regge action, quantum gravity
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