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q-Fock Space Representations of the q-Lorentz Algebra and Irreducible Tensors

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Symmetries in Science VI

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Abstract

We present the q-deformation of the Lorentz algebra, with Hopf structure, in terms of four independent harmonic oscillators. The explicit realization of the q-Fock space is given and the irreducible finite-dimensional representations of so(1,3)q are described and characterized by its two q-Casimir operators. The concept of irreducible q-Lorentz tensor is also introduced. The analysis is made for a real deformation parameter.

Lecture delivered (by J.A.) at the Symmetries in Science VI Symposium (Bregenz, August 2–7 (1992)) in honour of Professor L.C. Biedenharn. To appear in the Proceedings (B. Gruber Ed., Plenum Pub. Co.)

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Authors and Affiliations

  1. High Energy Physics Laboratory, Department of Physics, University of Helsinki, SF-00170, Helsinki, Finland

    M. Chaichian

  2. Departamento de Física Teórica and IFIC (CSIC), Universidad de Valencia, E-46100, Burjassot, Valencia, Spain

    J. A. De Azcárraga & F. Rodenas

Authors
  1. M. Chaichian
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  2. J. A. De Azcárraga
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  3. F. Rodenas
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Editor information

Editors and Affiliations

  1. Southern Illinois University at Carbondale in Niigata, Niigata, Japan

    Bruno Gruber

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© 1993 Springer Science+Business Media New York

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Chaichian, M., De Azcárraga, J.A., Rodenas, F. (1993). q-Fock Space Representations of the q-Lorentz Algebra and Irreducible Tensors. In: Gruber, B. (eds) Symmetries in Science VI. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-1219-0_14

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  • DOI: https://doi.org/10.1007/978-1-4899-1219-0_14

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4899-1221-3

  • Online ISBN: 978-1-4899-1219-0

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