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Algebraic expressions for classes of generalized 6-j and 9-j symbols for certain Lie groups

  • I. Representations Theory of Finite and Infinite Dimensional Groups
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Group Theoretical Methods in Physics

Part of the book series: Lecture Notes in Physics ((LNP,volume 313))

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Abstract

The 6-j and 9-j symbols that occur in angular-momentum theory can be generalized from the group S0(3) to other compact Lie groups. The initial motivation for doing so stems from the Jahn-Teller effect, where the Hamiltonian for a particular octahedral system possesses an approximate SO(5) symmetry. Several methods are described for finding formulas for multiplicity-free 6-j and 9-j symbols, including generalizations of Schwinger's generating functions. The recent method of Cerkaski for finding a class of 6-j symbols with one multiplicity index is illustrated with an example for Sp(6).

Talk presented at,the XVI International Colloquium on Group Theoretical Methods in Physics, Varna, June 1987.

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Authors and Affiliations

  1. Department of Physics and Astronomy, The Johns Hopkins University, 21218, Baltimore, MD, USA

    B. R. Judd

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  1. B. R. Judd
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Heinz-D. Doebner Jörg-D. Hennig Tchavdar D. Palev

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© 1988 Springer-Verlag

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Judd, B.R. (1988). Algebraic expressions for classes of generalized 6-j and 9-j symbols for certain Lie groups. In: Doebner, HD., Hennig, JD., Palev, T.D. (eds) Group Theoretical Methods in Physics. Lecture Notes in Physics, vol 313. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0012257

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  • DOI: https://doi.org/10.1007/BFb0012257

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-50245-6

  • Online ISBN: 978-3-540-45959-0

  • eBook Packages: Springer Book Archive

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