A new spin foam model for 4D gravity

By L. Freidel, K. Krasnov. 2007

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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.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/348daeceaa18d9ed8674d25d317f155ebaa413a9

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Citations in the corpus

Zakopane lectures on loop gravity (2011, background): “3) was found independently and developed during the last few years by a number of research groups [15, 16, 17, 18, 19, 20, 21], using different path and different formalisms (and a variety of notations).”
A Renormalizable 4-Dimensional Tensor Field Theory (2011, methodology): “In four dimensions more elaborate propagators have been proposed [25, 26, 27, 28] to implement the Plebanski simplicity constraints on the 4 dimensional Ooguri GFT or 4D BF theory.”
Twisted geometries: A geometric parametrisation of SU(2) phase space (2010, background): “The motivation for these labels comes from the coherent intertwiners introduced in [8] (for earlier ideas, see also [22]) and further developed in [13], which have proved useful to construct the new EPR-FK-LS spin foam models [9, 10], and crucial to study their semiclassical limit [12, 13, 14] and n”
Lorentzian spin foam amplitudes: graphical calculus and asymptotics (2009, methodology): “For γ < 1 the two constructions of [6, 7] and [8, 9] are equivalent, meaning one has both a LQG-like boundary space and an”
On the semiclassical limit of 4d spin foam models (2008, methodology): “As shown in [30], the spin foam models FKγ introduced in [26] and described in (3) can be written as Z ∆(jf ) = ∑”
The Spin-Foam Approach to Quantum Gravity (2012, methodology): “Freidel and Krasnov introduced the linear version of Plebanski constraints that where later used in order to provide a simpler derivation and generalization of the EPRL model to arbitrary Immirzi parameter.”
Towards spinfoam cosmology (2010, background): “The vertex amplitude is Wv(σ) = 〈Wv|ψv(σ)〉, where ψv(σ) is the spin network obtained by cutting σ with a small 3-sphere surrounding v and the the vertex amplitude that defines the dynamics of LQG is [2, 4, 5, 5, 6]”
Colored Group Field Theory (2009, unknown): “This line of research has been explored in [19–23], to define more realistic GFT’s whose semiclassical limit [24,25] exhibits the expected behavior.”
Area–angle variables for general relativity (2008, methodology): “Here we are imposing directly the solution in the geometric sector, so we do not comment about this ambiguity, which however plays an important role in quantum models [15, 20, 21].”
Spin-foams for all loop quantum gravity (2009, methodology): “On the other hand, the work that should be and will be considered closer in the spirit of the current paper is the Freidel–Krasnov model [15] (especially in the range of γ in which that model does not overlap with EPRL).”
Renormalization of Tensorial Group Field Theories: Abelian U(1) Models in Four Dimensions (2012, methodology): “In this context, models for 4d quantum gravity have been developed, the most interesting ones being found in [37–42].”