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Acceleration-enlarged symmetries in nonrelativistic space-time with a cosmological constant

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Abstract

By considering the nonrelativistic limit of de Sitter geometry one obtains the nonrelativistic space-time with a cosmological constant and Newton–Hooke (NH) symmetries. We show that the NH symmetry algebra can be enlarged by the addition of the constant acceleration generators and endowed with central extensions (one in any dimension (D) and three in D=(2+1)). We present a classical Lagrangian and Hamiltonian framework for constructing models quasi-invariant under enlarged NH symmetries that depend on three parameters described by three nonvanishing central charges. The Hamiltonian dynamics then splits into external and internal sectors with new noncommutative structures of external and internal phase spaces. We show that in the limit of vanishing cosmological constant the system reduces to the one, which possesses acceleration-enlarged Galilean symmetries.

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Authors and Affiliations

  1. Institute for Theoretical Physics, University of Wrocław, pl. Maxa Borna 9, 50–205, Wrocław, Poland

    J. Lukierski

  2. Department of Theoretical Physics, University of Valencia, 46100, Burjassot (Valencia), Spain

    J. Lukierski

  3. An der Krebskuhle 21, 33619, Bielefeld, Germany

    P.C. Stichel

  4. Department of Mathematical Sciences, University of Durham, South Road, Durham, DH1 3LE, UK

    W.J. Zakrzewski

Authors
  1. J. Lukierski
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  2. P.C. Stichel
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  3. W.J. Zakrzewski
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Correspondence to W.J. Zakrzewski.

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Lukierski, J., Stichel, P. & Zakrzewski, W. Acceleration-enlarged symmetries in nonrelativistic space-time with a cosmological constant . Eur. Phys. J. C 55, 119–124 (2008). https://doi.org/10.1140/epjc/s10052-008-0576-8

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  • DOI: https://doi.org/10.1140/epjc/s10052-008-0576-8

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