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A New Spin Foam Model for 4d Gravity

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arxiv 0708.1595 v2 pith:7VP77N37 submitted 2007-08-13 gr-qc

Laurent Freidel , Kirill Krasnov This is my paper · ORCID
classification gr-qc
keywords modelfoamspingravityformulationgravitationalsectortopological
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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 generalises 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 quantisation. 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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Cited by 6 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Renormalization group flows in area-metric gravity

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    The first renormalization group analysis of area-metric gravity shows shape-mismatching masses grow toward the infrared, parity is not emergent, and the Immirzi parameter flow has fixed points at γ=0 and γ=∞.

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    POVM-based conditioning on scalar-field quantum reference frames defines relational observables in group field theory that match prior number and volume results on coherent states.

  3. Quantum geometry from higher gauge theory

    gr-qc 2019-08 conditional novelty 7.0 of 10

    The BFCG-Yetter model and the KBF state sum produce the same single-4-simplex amplitude when evaluated on boundary states called G-networks.

  4. Deep learning spinfoam vertex amplitudes: the Euclidean Barrett-Crane model

    gr-qc 2025-05 conditional novelty 6.0 of 10

    A proof-of-principle that simple neural networks can learn Euclidean Barrett-Crane 10j vertex amplitudes: classification generalizes to higher cutoffs, regression works only within the trained low-spin domain.

  5. Consistency check on the fundamental and alternative flux operators in loop quantum gravity

    gr-qc 2019-08 conditional novelty 5.0 of 10

    A graphical consistency check between the fundamental and alternative flux operators in loop quantum gravity fixes the volume-operator constant κ_reg to 1/2.

  6. Les Houches lectures on Spinfoam Path Integrals

    gr-qc 2026-07 accept novelty 2.0 of 10

    A pedagogical review of spinfoam path integrals, from 1d quantum mechanics and 2d BF theory through Ponzano-Regge/Turaev-Viro to the 4d EPRL model, accurate but with no new results.

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