The DOI matches its Crossref record; 59 of the 63 references it cites were found in a registry or an index.
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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“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]
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“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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Citations
Cites
The analysis of linear partial differential operators
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Hörmander, L. (2007) · Classics in mathematics · doi:10.1007/978-3-540-49938-1 · Cited by 2,701
Rovelli, C. (2004) · doi:10.1017/cbo9780511755804 · Cited by 2,240
The Analysis of Linear Partial Differential Operators I
Hörmander, L. (2003) · Classics in mathematics · doi:10.1007/978-3-642-61497-2 · Cited by 1,493
Ribbon graphs and their invaraints derived from quantum groups
Reshetikhin, N., & Turaev, V. G. (1990) · Communications in Mathematical Physics · doi:10.1007/bf02096491 · Cited by 1,017
LQG vertex with finite Immirzi parameter
Engle, J., Livine, E., Pereira, R., & Rovelli, C. (2008) · Nuclear Physics B · doi:10.1016/j.nuclphysb.2008.02.018 · Cited by 584
A new spin foam model for 4D gravity
Freidel, L., & Krasnov, K. (2008) · Classical and Quantum Gravity · doi:10.1088/0264-9381/25/12/125018 · Cited by 521
Relativistic Spin Networks and Quantum GravityPreprint
Barrett, J. W., Crane, L., & Crane, J. W. B. L. (1998) · Cited by 423
Self-citation
Research works printed but not linked: 2
- Ponzano G, 1968, Spectroscopy and Group Theoretical Methods in Physics, 1
- Gelfand I, 1966, Generalized Functions: Vol 5. Integral Geometry and Representation Theory
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Mansuroglu, R., & Sahlmann, H. (2023) · Journal of High Energy Physics · doi:10.1007/jhep02(2023)062 · Cited by 3
Metadata
- 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 › Nuclear and High Energy 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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