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

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


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.


Hilbert Space Matrix Element Normal Subgroup Representation Theory Representation Space 
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Copyright information

© Springer-Verlag 1976

Authors and Affiliations

  • R. Dirl
    • 1
  1. 1.Technische Hochschule1.Institut für theoretische PhysikViennaAustria

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