LQG vertex with finite Immirzi parameter

By Jonathan Engle, Etera R. Livine, Roberto Pereira, Carlo Rovelli. 2007

618 citations recorded by the source corpus.

Abstract We extend the definition of the “flipped” loop-quantum-gravity vertex to the case of a finite Immirzi parameter γ . We cover both the Euclidean and Lorentzian cases. We show that the resulting dynamics is defined on a Hilbert space isomorphic to the one of loop quantum gravity, and that the area operator has the same discrete spectrum as in loop quantum gravity. This includes the correct dependence on γ , and, remarkably, holds in the Lorentzian case as well. The ad hoc flip of the symplectic structure that was required to derive the flipped vertex is not anymore required for finite γ . These results establish a bridge between canonical loop quantum gravity and the spinfoam formalism in four dimensions.

Subfields: Geometry and Topology, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/f015aeff45d70d93860c0bfaa4c896892400f635

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Citations in the corpus

Zakopane lectures on loop gravity (2011, background): “31) which is precisely based on Regge calculus, and a single vertex is interpreted as a flat 4-simplex [18, 20].”
Twisted geometries: A geometric parametrisation of SU(2) phase space (2010, background): “On the other hand, the spin foam graviton calculations [5, 6] and recent progress in the spin foam formalism [7, 8, 9, 10, 11, 12, 13, 14], suggest a different approach to the question, where one attempts at describing a classical phase space point in terms of quantities referring to discrete geomet”
Area–angle variables for general relativity (2008, background): “Recently, a spinfoam model has been proposed [15] (see also [25]), whose dynamical variables can be expressed as normals to triangles [20] (see also [21]).”
The Spin-Foam Approach to Quantum Gravity (2012, methodology): “The previous is the form of the EPRL model as derived in [164].”
Towards spinfoam cosmology (2010, background): “[5] Jonathan Engle, Etera Livine, Roberto Pereira, and Carlo Rovelli.”
On the semiclassical limit of 4d spin foam models (2008, background): “Lorentzian versions of these models have been constructed as well [26, 28, 29].”
Asymptotic analysis of the EPRL four-simplex amplitude (2009, methodology): “Firstly, the asymptotics for the Lorentzian models [15, 31] should be computed.”
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].”
A new look at loop quantum gravity (2010, neutral): “In fact, there is a derivation of the vertex (45) which is precisely based on Regge calculus, and a single vertex is interpreted as a flat 4-simplex [33, 40].”
Spin-foams for all loop quantum gravity (2009, methodology): “Finally, we generalize the Engle–Pereira–Rovelli–Livine intertwiner to the general spin-foams.”
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.”