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How-To compute EPRL spin foam amplitudes

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arxiv 2202.04360 v3 pith:LS6E4UNK submitted 2022-02-09 gr-qc

classification gr-qc
keywords foamspintransitionamplitudeamplitudesapproachcalculationsguide
verification ladder T0 review T1 audit T2 compute T3 formal

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Spin foam theory is a concrete framework for quantum gravity where numerical calculations of transition amplitudes are possible. Recently, the field became very active, but the entry barrier is steep, mainly because of its unusual language and notions scattered around the literature. This paper is a pedagogical guide to spin foam transition amplitude calculations. We show how to write an EPRL-FK transition amplitude, from the definition of the 2-complex to its numerical implementation using \texttt{sl2cfoam-next}. We guide the reader using an explicit example balancing mathematical rigor with a practical approach. We discuss the advantages and disadvantages of this approach and provide a novel look at a recently proposed approximation scheme.

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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. Thermal $n$-Point Conformal Blocks in Four Dimensions from Oscillator Representations

    hep-th 2025-07 conditional novelty 6.0 of 10

    New analytic formulas for four-dimensional thermal n-point conformal blocks are derived from oscillator representations, with a correct low-temperature limit to vacuum comb-channel blocks.

  2. 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.

  3. 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.

  4. (2+1) Lorentzian quantum cosmology from spin-foams: opportunities and obstacles for semi-classicality

    gr-qc 2024-11 conditional novelty 6.0 of 10

    A 2+1 Lorentzian spin-foam cosmology model with a Hessian-derived measure and a massive scalar field yields convergent partition functions, with semi-classical expectation values only in the causally regular sector an...

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