Lorentzian spin foam amplitudes: graphical calculus and asymptotics
Open accessAbstract
The amplitude for the 4-simplex in a spin foam model for quantum gravity is defined using a graphical calculus for the unitary representations of the Lorentz group. The asymptotics of this amplitude are studied in the limit when the representation parameters are large, for various cases of boundary data. It is shown that for boundary data corresponding to a Lorentzian simplex, the asymptotic formula has two terms, with phase plus or minus the Lorentzian signature Regge action for the 4-simplex geometry, multiplied by an Immirzi parameter. Other cases of boundary data are also considered, including a surprising contribution from Euclidean signature metrics.
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The Lorentzian EPRL asymptotic formula has two terms, corresponding to a parity-related 4-simplex.
“To each solution one can associate a second solution corresponding to a parity related 4-simplex and, consequently, the asymptotic formula has two terms.”
From The Spin-Foam Approach to Quantum Gravity (2013) · cites this paper as [64]
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 [64]
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- Authors
- Barrett, J. W., Dowdall, R. J., Fairbairn, W. J., Hellmann, F., & Pereira, R.
- Affiliations
- University of Nottingham (GB)
- Venue
- Classical and Quantum Gravity
- Publisher
- IOP Publishing
- Published
- 2010-07-07
- Volume
- 27
- Issue
- 16
- Pages
- 165009
- ISSN
- 0264-9381 (ISSN-L)
- 1361-6382
- OpenAlex
- W2069556809
- Cited by
- 247
- References
- 63
- Citations by year
- 2026: 5 · 2025: 8 · 2024: 14 · 2023: 14 · 2022: 10 · 2021: 13 · 2020: 9 · 2019: 13 · 2018: 17 · 2017: 11 · 2016: 14 · 2015: 8 · 2014: 18 · 2013: 26 · 2012: 23
- FWCI
- 21.10
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Classical and Quantum Gravity (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- HAL (submittedVersion)
- HAL (submittedVersion, other-oa)
- Trinity's Access to Research Output (TARA) (Trinity College Dublin) (submittedVersion)
- arXiv (Cornell University)
- Funders
- Science and Technology Facilities Council (ST/G000417/1, ST/G00059X/1)
- 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
- graphical calculus, asymptotic analysis, quantum gravity, spin foam models, Lorentzian quantum gravity
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