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The Hilbert space L2(SU(2)) as a representation space for the group (SU(2) × SU(2)) Ⓢ S2

  • Mathematical Physics
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Group Theoretical Methods in Physics

Part of the book series: Lecture Notes in Physics ((LNP,volume 50))

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Abstract

The Hilbert space L2(SU(2)) is used as a representation space for a (unitary) representation of the semi-direct product group (SU(2) × SU(2))ⓈS2 and the corresponding group algebra. Special operators are constructed which are closely related to the representation theory of the groups SU(2) and S2 and are irreducible tensor operators with respect to (SU(2) × SU(2)) Ⓢ S2. These operators are then used to define complete sets of irreducible tensor operators, to derive correlations between such special operators and to calculate two classes of Clebsch-Gordan coefficients of (SU(2) × SU(2)) Ⓢ S2. The results obtained for SU(2) can be generalized in a systematic way for any finite or compact continuous group.

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Authors and Affiliations

  1. Technische Hochschule, 1.Institut für theoretische Physik, Vienna, Austria

    R. Dirl

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  1. R. Dirl
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Editor information

A. Janner T. Janssen M. Boon

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© 1976 Springer-Verlag

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Dirl, R. (1976). The Hilbert space L2(SU(2)) as a representation space for the group (SU(2) × SU(2)) Ⓢ S2 . In: Janner, A., Janssen, T., Boon, M. (eds) Group Theoretical Methods in Physics. Lecture Notes in Physics, vol 50. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-07789-8_48

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  • DOI: https://doi.org/10.1007/3-540-07789-8_48

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-07789-3

  • Online ISBN: 978-3-540-38252-2

  • eBook Packages: Springer Book Archive

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