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A Lorentzian Signature Model for Quantum General Relativity

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arxiv gr-qc/9904025 v3 pith:4CEV6PPF submitted 1999-04-09 gr-qc

John W. Barrett , Louis Crane This is my paper · ORCID
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We give a relativistic spin network model for quantum gravity based on the Lorentz group and its q-deformation, the Quantum Lorentz Algebra. We propose a combinatorial model for the path integral given by an integral over suitable representations of this algebra. This generalises the state sum models for the case of the four-dimensional rotation group previously studied in gr-qc/9709028. As a technical tool, formulae for the evaluation of relativistic spin networks for the Lorentz group are developed, with some simple examples which show that the evaluation is finite in interesting cases. We conjecture that the `10J' symbol needed in our model has a finite value.

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Cited by 4 Pith papers

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

  1. A state sum for four-dimensional Lorentzian quantum geometry in terms of edge vectors

    gr-qc 2025-01 conditional novelty 6.0 of 10

    A new state sum model for 4D Lorentzian quantum gravity is constructed from quantum edge vectors and related to the Barrett-Crane spin foam model.

  2. Spinfoams, $\gamma$-duality and parity violation in primordial gravitational waves

    gr-qc 2024-03 unverdicted novelty 6.0 of 10

    γ-duality in the EPRL spinfoam model determines the relation between parity-even and parity-odd terms in an effective gravity theory, allowing the Barbero-Immirzi parameter to be measured from inflationary tensor observables.

  3. Causal structure in spin-foams

    gr-qc 2021-09 unverdicted novelty 5.0 of 10

    Proposes a causal EPRL spin-foam model where the two-complex orientation encodes causality and aids semiclassical geometry reconstruction.

  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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