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Relativistic spin networks and quantum gravity

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arxiv gr-qc/9709028 v2 pith:XQDPQ5IJ submitted 1997-09-12 gr-qc hep-th

John W. Barrett , Louis Crane This is my paper
classification gr-qchep-th
keywords spinnetworksquantumrelativisticdimensionalgravitygeometryrelated
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Relativistic spin networks are defined by considering the spin covering of the group SO(4), SU(2) times SU(2). Relativistic quantum spins are related to the geometry of the 2-dimensional faces of a 4-simplex. This extends the idea of Ponzano and Regge that SU(2) spins are related to the geometry of the edges of a 3-simplex. This leads us to suggest that there may be a 4-dimensional state sum model for quantum gravity based on relativistic spin networks which parallels the construction of 3-dimensional quantum gravity from ordinary spin networks.

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Cited by 2 Pith papers

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  1. Triangulating quantum gravity in AdS$_3$

    hep-th 2025-07 conditional novelty 6.0 of 10

    The fixed-angle gravitational path integral in AdS3 equals a Conformal Turaev-Viro partition function, the fixed-length path integral equals a Virasoro TQFT amplitude squared, and the semiclassical geometries are buil...

  2. 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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