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Symmetries in Science VII pp 535–543Cite as

Spectrum Generating q-Algebras for Anyons

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Abstract

We review some of the uses of the spectrum generating algebra approach using conventional Lie algebras applied to exactly solvable many-body models. We compare these to the possible applications of spectrum generating q-algebras. We describe a generalized deformation of the canonical commmutation relations (CCR), which reduce both to the CCR for standard q-bosons, and to the Canonical Anti-commutation Relations (CAR) for fermions in appropriate limits. By a choice of the deformation, we show that the new “qummutation relations” define bosonic-type particles having finite number occupancy (anyons) and relate these to standard descriptions of anyons, and use them to construct a model hamiltonian for interacting anyons which has the quantum group SU q (2) as dynamical group.

To Franco Iachello, who has shown us that experiment is the motive force of theory.

Talk contributed to SYMMETRIES IN SCIENCE VII: Spectrmn Generating Algebras and Dynamic Symmetries in Physics, on the occasion of the fiftieth birthday of Professor Franco Iachello.

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Author information

Authors and Affiliations

  1. Faculty of Mathematics, The Open University, Milton Keynes, MK7 6AA, UK

    Allan I. Solomon

  2. Department of Physics, City College of the City University of New York, New York, 10031, USA

    Joseph L. Birman

Authors
  1. Allan I. Solomon
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  2. Joseph L. Birman
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Editor information

Editors and Affiliations

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

    Bruno Gruber

  2. University of Tokyo, Tokyo, Japan

    Takaharu Otsuka

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© 1994 Springer Science+Business Media New York

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Solomon, A.I., Birman, J.L. (1994). Spectrum Generating q-Algebras for Anyons. In: Gruber, B., Otsuka, T. (eds) Symmetries in Science VII. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-2956-9_46

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  • DOI: https://doi.org/10.1007/978-1-4615-2956-9_46

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4613-6285-2

  • Online ISBN: 978-1-4615-2956-9

  • eBook Packages: Springer Book Archive

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