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Semi-Classical Limits of Simplicial Quantum Gravity

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arxiv gr-qc/9310016 v1 pith:V37PA7YT submitted 1993-10-08 gr-qc hep-th

J.W. Barrett , T.J. Foxon This is my paper · ORCID
classification gr-qchep-th
keywords simplicialeuclideangeometrygravityinterpretationlorentzianstate-sumdimensions
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abstract

We consider the simplicial state-sum model of Ponzano and Regge as a path integral for quantum gravity in three dimensions. We examine the Lorentzian geometry of a single 3-simplex and of a simplicial manifold, and interpret an asymptotic formula for $6j$-symbols in terms of this geometry. This extends Ponzano and Regge's similar interpretation for Euclidean geometry. We give a geometric interpretation of the stationary points of this state-sum, by showing that, at these points, the simplicial manifold may be mapped locally into flat Lorentzian or Euclidean space. This lends weight to the interpretation of the state-sum as a path integral, which has solutions corresponding to both Lorentzian and Euclidean gravity in three dimensions.

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Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. OpenAlex reports about 66 citations worldwide. Full citation record

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

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    gr-qc 2024-11 conditional novelty 6.0 of 10

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  4. 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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