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Towards Finite Quantum Field Theory in Non-Commutative Geometry

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arxiv hep-th/9505175 v1 pith:WHJ7OBAI submitted 1995-05-29 hep-th

H. Grosse , C. Klimcik , P. Presnajder This is my paper · ORCID
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keywords fieldfinitespheretheoryapproachautomaticallydescribeexplicitely
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We describe the self-interacting scalar field on the truncated sphere and we perform the quantization using the functional (path) integral approach. The theory posseses a full symmetry with respect to the isometries of the sphere. We explicitely show that the model is finite and the UV-regularization automatically takes place.

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Cited by 4 Pith papers

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    Horizon partons on the fuzzy sphere form lowest-Landau-level states under an intrinsic Berry monopole, generating Ohmic, Hall and polarization currents that a link-field condensate locks to the bulk Maxwell field, yie...

  2. Quantum simulation of gauge theories on dynamical spacetimes via Floquet-induced matrix models

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    Ensemble-averaged Floquet fidelities of Haar-random states reproduce Euclidean Yang-Mills matrix path-integral weights at leading order, enabling lattice-free quantum simulation of gauge fields on dynamical geometries.

  3. 3d Conformal Field Theories via Fuzzy Sphere Algebra

    cond-mat.str-el 2026-02 conditional novelty 6.0 of 10

    The fuzzy-sphere density-mode algebra is a genuine Lie algebra, but a direct density-mode realization of the 3d conformal algebra so(3,2) exists only for the two-electron system.

  4. Minimal covariant quantum space-time

    hep-th 2025-02 conditional novelty 6.0 of 10

    The minimal covariant quantum space-time M^{1,3}_0 is shown to be a quantized twistor space, an S2 bundle over a k=-1 FLRW space-time, with localized quasi-coherent states.

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