Noncommutative spherically symmetric spaces

Murray, Sean; Govaerts, Jan

doi:10.1103/PHYSREVD.83.025009

Title: Noncommutative spherically symmetric spaces

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Abstract

We examine some noncommutative spherically symmetric spaces in three space dimensions. A generalization of Snyder's noncommutative (Euclidean) space allows the inclusion of the generator of dilations into the defining algebra of the coordinate and rotation operators. We then construct a spherically symmetric noncommutative Laplacian on this space having the correct limiting spectrum. This is presented via a creation and annihilation operator realization of the algebra, which may lend itself to a truncation of the Hilbert space.

Authors:

Murray, Sean; Govaerts, Jan ^[1]

Centre for Cosmology, Particle Physics and Phenomenology, Universite catholique de Louvain, Chemin du Cyclotron 2, B-1348 Louvain-la-Neuve (Belgium)

Publication Date:: Sat Jan 15 00:00:00 EST 2011

OSTI Identifier:: 21503983

Resource Type:: Journal Article

Journal Name:: Physical Review. D, Particles Fields

Additional Journal Information:: Journal Volume: 83; Journal Issue: 2; Other Information: DOI: 10.1103/PhysRevD.83.025009; (c) 2011 American Institute of Physics; Journal ID: ISSN 0556-2821

Country of Publication:: United States

Language:: English

Subject:: 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ANNIHILATION OPERATORS; COMMUTATION RELATIONS; EUCLIDEAN SPACE; HILBERT SPACE; LAPLACIAN; ROTATION; SPECTRA; SYMMETRY; BANACH SPACE; MATHEMATICAL OPERATORS; MATHEMATICAL SPACE; MOTION; QUANTUM OPERATORS; RIEMANN SPACE; SPACE

Citation Formats


                    Murray, Sean, Govaerts, Jan, and Centre for Cosmology, Particle Physics and Phenomenology, Universite catholique de Louvain, Chemin du Cyclotron 2, B-1348 Louvain-la-Neuve. Noncommutative spherically symmetric spaces.  United States: N. p., 2011. 
        Web.  doi:10.1103/PHYSREVD.83.025009.

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                    Murray, Sean, Govaerts, Jan, & Centre for Cosmology, Particle Physics and Phenomenology, Universite catholique de Louvain, Chemin du Cyclotron 2, B-1348 Louvain-la-Neuve. Noncommutative spherically symmetric spaces.  United States.  https://doi.org/10.1103/PHYSREVD.83.025009

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                    Murray, Sean, Govaerts, Jan, and Centre for Cosmology, Particle Physics and Phenomenology, Universite catholique de Louvain, Chemin du Cyclotron 2, B-1348 Louvain-la-Neuve. 2011.  
        "Noncommutative spherically symmetric spaces".  United States.  https://doi.org/10.1103/PHYSREVD.83.025009.

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@article{osti_21503983,

  title        = {Noncommutative spherically symmetric spaces},

  author       = {Murray, Sean and Govaerts, Jan and Centre for Cosmology, Particle Physics and Phenomenology, Universite catholique de Louvain, Chemin du Cyclotron 2, B-1348 Louvain-la-Neuve},

  abstractNote = {We examine some noncommutative spherically symmetric spaces in three space dimensions. A generalization of Snyder's noncommutative (Euclidean) space allows the inclusion of the generator of dilations into the defining algebra of the coordinate and rotation operators. We then construct a spherically symmetric noncommutative Laplacian on this space having the correct limiting spectrum. This is presented via a creation and annihilation operator realization of the algebra, which may lend itself to a truncation of the Hilbert space.},

  doi          = {10.1103/PHYSREVD.83.025009},

  url          = {https://www.osti.gov/biblio/21503983},
  journal      = {Physical Review. D, Particles Fields},

  issn         = {0556-2821},

  number       = 2,

  volume       = 83,

  place        = {United States},

  year         = {Sat Jan 15 00:00:00 EST 2011},

  month        = {Sat Jan 15 00:00:00 EST 2011}

}

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https://doi.org/10.1103/PHYSREVD.83.025009

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