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Group field theory on quantum groups

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arxiv 2205.13312 v1 pith:YSAR3YKN submitted 2022-05-26 hep-th gr-qc

Florian Girelli , Matteo Laudonio This is my paper · ORCID
classification hep-thgr-qc
keywords fieldgrouptheoryalgebracaseconstantcosmologicalhaft
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We introduce the framework of Hopf algebra field theory (HAFT) which generalizes the notion of group field theory to the quantum group (Hopf algebra) case. We focus in particular on the 3d case and show how the HAFT we considered is topological. The highlight of the construction is the notion of plane-wave which leads, in the specific example of SUq (2) with q real, to a discretization of the Euclidian BF action with a negative cosmological constant. This work can be viewed as the generalization of the seminal work by Baratin and Oriti: we have a (non-commutative) formulation of simplicial 3d gravity in the presence of a non-zero cosmological constant.

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Cited by 2 Pith papers

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

  1. Indefinite probabilities in quantum spacetime: A deepening of unpredictability

    quant-ph 2026-05 unverdicted novelty 7.0 of 10

    Using the SU_q(2) quantum group for spin rotations yields non-commuting probability operators, implying indefinite probabilities and preventing sharp determination of relative observer orientations.

  2. Doubly Quantum Mechanics

    quant-ph 2024-12 conditional novelty 6.0 of 10

    Replacing SU(2) with SU_q(2) turns measurement probabilities into operators and makes reference-frame alignment between two observers fundamentally imprecise even in the limit of infinitely many exchanged spins.

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