A new spin foam model for 4D gravity
Open accessAbstract
Starting from Plebanski formulation of gravity as a constrained BF theory we propose a new spin foam model for 4D Riemannian quantum gravity that generalizes the well-known Barrett–Crane model and resolves the inherent to it ultra-locality problem. The BF formulation of 4D gravity possesses two sectors: gravitational and topological ones. The model presented here is shown to give a quantization of the gravitational sector, and is dual to the recently proposed spin foam model of Engle et al which, we show, corresponds to the topological sector. Our methods allow us to introduce the Immirzi parameter into the framework of spin foam quantization. We generalize some of our considerations to the Lorentzian setting and obtain a new spin foam model in that context as well.
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The logic used in the derivation of the Freidel-Krasnov models is different from that of the EPRL model.
“However, the logic used in the derivation is different.”
From The Spin-Foam Approach to Quantum Gravity (2013) · cites this paper as [182]
The Freidel-Krasnov idea is to express the BF path integral in terms of the coherent state representation in order to impose the Plebanski constraints semiclassically in terms of expectation values.
“The idea is to express the BF path integral in terms of the coherent state representation, in order to impose the Plebanski constraints semiclassically in terms of expectation values.”
From The Spin-Foam Approach to Quantum Gravity (2013) · cites this paper as [182]
Freidel and Krasnov introduced the linear version of the Plebanski constraints that was later used to provide a simpler derivation and generalization of the EPRL model to arbitrary Immirzi parameter.
“Freidel and Krasnov introduced11 the linear version of the Plebanski constraints that later used in order to provide a simpler derivation and generalization of the EPRL model to arbitrary Immirzi parameter.”
From The Spin-Foam Approach to Quantum Gravity (2013) · cites this paper as [182]
The Hamiltonian analysis of constrained BF theory is central to the replacement of the Plebanski quadratic constraints by linear ones, which has been useful for defining the new vertex amplitudes.
“As we show below, the Hamiltonian analysis of such a formulation of gravity is at the heart of the replacement of the Plebanski quadratic constraints by linear ones that has been so useful in the definition of the new vertex amplitudes [182].”
From The Spin-Foam Approach to Quantum Gravity (2013) · cites this paper as [182]
The Freidel-Krasnov models are arguably the same as the EPRL model for a suitable range of the Immirzi parameter, with vertex amplitudes coinciding for γ < 1.
“Indeed, these models are arguably the same as the EPRL model for a suitable range of the Immirzi parameter (the vertex amplitudes coincide for γ < 1 as we will discuss in the sequel).”
From The Spin-Foam Approach to Quantum Gravity (2013) · cites this paper as [182]
Freidel and Krasnov independently introduced a very similar set of models.
“A very similar set of models were independently introduced by Freidel and Krasnov in [182].”
From The Spin-Foam Approach to Quantum Gravity (2013) · cites this paper as [182]
The quadratic simplicity constraints are equivalent in the discrete setting to a linear simplicity constraint on each face of a tetrahedron.
“As first emphasized in [182], the quadratic simplicity constraints (25) — and more precisely in their dual version presented below (154) — are equivalent in the discrete setting to the linear constraint on each face of a given tetrahedron 126”
From The Spin-Foam Approach to Quantum Gravity (2013) · cites this paper as [182]
There exists an over-complete basis of SU(2) coherent states labeled by group elements g in SU(2).
“There exists an over-complete basis ∣j, g⟩ ∈ ℋj labeled by g ∈ SU(2) such that 108”
From The Spin-Foam Approach to Quantum Gravity (2013) · cites this paper as [182]
Freidel and Krasnov introduced new four-dimensional gravity spin-foam models using the coherent state basis of the Livine-Speziale quantum tetrahedron.
“Freidel and Krasnov [182] introduced a set of new spin-foam models for four-dimensional gravity using the coherent state basis of the quantum tetrahedron of Livine and Speziale [254].”
From The Spin-Foam Approach to Quantum Gravity (2013) · cites this paper as [182]
The vertex amplitude for the EPRL/FK models is given by equation (30), with unbalanced spins j±_ab = γ± j_ab and γ± = (1 ± γ)/2.
“where the unbalanced spins j + , j -are j ± ab = γ ± j ab , γ ± = 1 ± γ 2 . (31”
From LQG propagator from the new spin foams (2009) · cites this paper as [20]
For Euclidean signature and Immirzi parameter 0 < γ < 1, the EPRL γ and FK γ spin foam models coincide.
“We restrict attention to Euclidean signature and Immirzi parameter smaller than one: 0 < γ < 1.In this case the two models coincide.”
From LQG propagator from the new spin foams (2009) · cites this paper as [20]
In the limit γ → ∞, the FK model is no longer the BC model.
“In particular γ →∞ is no longer the BC model [21].”
From Spin-foams for all loop quantum gravity (2010) · cites this paper as [21]
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- Authors
- Freidel, L., & Krasnov, K.
- Affiliations
- Perimeter Institute (CA)
- University of Nottingham (GB)
- Venue
- Classical and Quantum Gravity
- Publisher
- IOP Publishing
- Published
- 2008-06-03
- Volume
- 25
- Issue
- 12
- Pages
- 125018
- ISSN
- 0264-9381 (ISSN-L)
- 1361-6382
- OpenAlex
- W2058578933
- Cited by
- 521
- References
- 31
- Citations by year
- 2026: 4 · 2025: 10 · 2024: 17 · 2023: 21 · 2022: 14 · 2021: 46 · 2020: 35 · 2019: 20 · 2018: 18 · 2017: 16 · 2016: 25 · 2015: 12 · 2014: 27 · 2013: 43 · 2012: 45
- FWCI
- 42.13
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Classical and Quantum Gravity (publishedVersion)
- arXiv (Cornell University) (publishedVersion)
- 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, 4D quantum gravity, BF theory, Barrett-Crane model, Immirzi parameter, topological sectors
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