The asymptotics of an amplitude for the 4-simplex
Open accessAbstract
An expression for the oscillatory part of an asymptotic formula for the relativistic spin network amplitude for a 4-simplex is given.The amplitude depends on specified areas for each two-dimensional face in the 4-simplex.The asymptotic formula has a contribution from each flat Euclidean metric on the 4-simplex which agrees with the given areas.The oscillatory part of each contribution is determined by the Regge calculus Einstein action for that geometry.
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The interaction vertex (10j symbol, or Barrett-Crane vertex amplitude) has been shown to include, beside the 'good' term approximating the exponential of the Einstein-Hilbert action, two 'bad' terms: an exponential with opposite sign giving the cosine of the Regge action, and a dominant term depending on the existence of degenerate four-simplices.
“The physical correctness of these theories has been questioned because in the low-energy limit their interaction vertex (10 j symbol, or Barrett-Crane vertex amplitude) has been shown to include -beside the 'good' term approximating the exponential of the Einstein-Hilbert action [19]- also two 'bad' terms: an exponential with opposite sign, giving the cosine of Regge action [19] (analogous to the”
From Graviton Propagator from Background-Independent Quantum Gravity (2006) · cites this paper as [20]
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References 6 · Cited by 108
Research works printed but not linked: 3
- J.W. Barrett, L. Crane, Relativistic spin networks and quantum gravity gr-qc/9709028 J. Math. Phys. 39 (1998), 3296-3302. · arXiv
- J.C. Baez, Spin foam models, Class. Quant. Grav. 15(1998), 1827-1858.
- G. Ponzano and T. Regge, Semiclassical limit of Racah coefficients, Spectroscopic and group theoretical methods in Physics (F. Bloch, ed.), North-Holland, 1968, pp. 1-58.
- Authors
- Barrett, J. W., & Williams, R. M.
- Affiliations
- Pennsylvania State University (US)
- Venue
- Advances in Theoretical and Mathematical Physics
- Publisher
- International Press of Boston
- Published
- 1999
- Volume
- 3
- Issue
- 2
- Pages
- 209-215
- ISSN
- 1095-0753 (ISSN-L)
- 1095-0761
- OpenAlex
- W2135387164
- Cited by
- 108
- References
- 6
- Citations by year
- 2026: 1 · 2025: 1 · 2024: 2 · 2023: 6 · 2022: 2 · 2021: 2 · 2020: 3 · 2019: 1 · 2018: 4 · 2015: 2 · 2014: 2 · 2013: 6 · 2012: 4
- FWCI
- 6.20
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Advances in Theoretical and Mathematical Physics (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- Nottingham ePrints (University of Nottingham) (submittedVersion, cc-by)
- Repository@Nottingham (University of Nottingham) (submittedVersion, cc-by)
- Repository@Nottingham (University of Nottingham) (submittedVersion, other-oa)
- 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
- 4-simplex, asymptotic formula, Regge calculus, Einstein-Hilbert action, face area, quantum gravity, simplicial geometry
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