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so (4) Plebanski action and relativistic spin-foam model
Open accessAbstract
We study the correspondence between the `relativistic spin-foam' model introduced by Barrett, Crane and Baez and the so (4) Plebanski action. We argue that the so (4) Plebanski model is the continuum analogue of the relativistic spin-foam model. We prove that the so (4) Plebanski action possesses four phases, one of which is related to gravity and discuss the relation between this model and the model of Euclidean tetrad gravity. We also show that the so (4) Plebanski model possesses another natural discretization that can be associated with another, new, spin-foam model which appear to be the so (4) counterpart of the spin-foam model describing the self-dual formulation of gravity.
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In the citing paper
“The construction of the generalized matrix models gives probably a path to follow in this direction, since the coupling of matter fields to gravity was already studied in the context of two-dimensional matrix models [109,115,116].”
From Spacetime geometry from algebra: spin foam models for non-perturbative quantum gravity (2001) · cites this paper as [109]
Experimental — accuracy not yet measuredIn the citing paper
“They can then be translated into the so-called simplicity constraints restricting the used SL (2 , C ) representations to simple ones, which have a vanishing quadratic Casimir operator [27, 25, 26].”
From SU(2)loop quantum gravity seen from covariant theory (2003) · cites this paper as [26]
In the citing paper
“Its construction relies on methods from geometrical quantization [21, 23], but can also be related to the generalised Palatini action (with Immirzi parameter) through a generalised constrained BF theory [24, 25, 26].”
From SU(2)loop quantum gravity seen from covariant theory (2003) · cites this paper as [26]
In the citing paper
“Similarly, the spin foam quantization, which can be understood as a discrete path integral, of the generalized Hilbert-Palatini action was shown not to depend on the Immirzi parameter [25, 26].”
From SU(2)loop quantum gravity seen from covariant theory (2003) · cites this paper as [26]
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Metadata
- Authors
- Pietri, R. D., & Freidel, L.
- Affiliations
- University of Parma (IT)
- École Normale Supérieure de Lyon (FR)
- Venue
- Classical and Quantum Gravity
- Publisher
- IOP Publishing
- Published
- 1999-01-01
- Volume
- 16
- Issue
- 7
- Pages
- 2187-2196
- ISSN
- 0264-9381 (ISSN-L)
- 1361-6382
- OpenAlex
- W2071979448
- Cited by
- 182
- References
- 20
- Citations by year
- 2026: 1 · 2025: 4 · 2024: 4 · 2023: 5 · 2022: 3 · 2021: 5 · 2020: 3 · 2019: 5 · 2018: 6 · 2016: 6 · 2015: 2 · 2014: 6 · 2013: 8 · 2012: 12
- FWCI
- 5.13
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Classical and Quantum Gravity (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- arXiv (Cornell University)
- Funders
- Centre National de la Recherche Scientifique
- 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
- Barrett-Crane model, self-dual gravity, continuum limit, quantum gravity
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