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Angular momentum in tensor representations ofU (3)

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Abstract

The problem of labelling the representations ofSO(3) contained in each representation ofU(3) is solved by using for this purpose an operatorZ with integral eigenvalues. A description is given of the decomposition of any tensor representation ofU(3) intoSO(3)-irreducible tensors labelled by these eigenvalues. An implicit definition ofZ is given in terms of theU(3) generators, and the relationship ofZ to the labelling operators (with irrational eigenvalues) proposed by Racah and others is made clear. A possible application to a quark model of the hadrons is described.

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Author notes

  1. A. J. Bracken

    Present address: Mathematics Department, University of Queensland, St. Lucia, Queensland

Authors and Affiliations

  1. Department of Mathematical Physics, University of Adelaide, 5001, Adelaide, S. Australia

    H. S. Green & A. J. Bracken

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  1. H. S. Green
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  2. A. J. Bracken
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Green, H.S., Bracken, A.J. Angular momentum in tensor representations ofU (3). Int J Theor Phys 11, 157–173 (1974). https://doi.org/10.1007/BF01809566

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  • DOI: https://doi.org/10.1007/BF01809566

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