Classification of Wigner Operators by a New Type of Weight Space Diagram

  • L. C. Biedenharn
  • J. D. Louck


It is quite appropriate that we commemorate Einstein with a conference devoted to symmetry in physics, since emphasis on the importance of symmetry concepts in theoretical physics is indeed one of Einstein’s many legacies. I would like to begin by emphasizing that the practical applications of symmetry techniques in physics have, in the final analysis, depended (explicitly or implicitly) upon the use of the Wigner coefficients of the symmetry group. Physically interesting operators are, in this approach, classified by the symmetry as instances of generic tensor operators and the matrix elements of the generic operators define the relevant Wigner coefficients. This is a concept whose depth and importance is common knowledge among the participants of this conference.


Null Space Tensor Operator Operator Pattern Boson Operator WIGNER Operator 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References and Footnotes

  1. 1.
    S.J. Alisauskas, A.-A.A. Jucys and A.P. Jucys, J. Math. Phys. 13 (1972) 1349.MathSciNetADSGoogle Scholar
  2. 2.
    G.E. Baird and L.C. Biedenharn, J. Math. Phys. 5 (1964) 1730.MathSciNetADSCrossRefGoogle Scholar
  3. 3.
    V.Bargmann and M.Moshinsky,Nucl.Phys.18(1960)697;23(1961)177.Google Scholar
  4. 4.
    E. Chacon, M. Ciftan and L.C. Biedenharn, J. Math. Phys. 13 (1972) 577.MathSciNetADSMATHCrossRefGoogle Scholar
  5. 5.
    Biedenharn, Louck, Chacon and Ciftan, J. Math. Phys. 13 (1972) 1957.MathSciNetADSMATHCrossRefGoogle Scholar
  6. 6.
    C.J. Hinrich, J. Math. Phys. 16 (1975) 2271.ADSCrossRefGoogle Scholar
  7. 7.
    M. Moshinsky, Rev. Mod. Phys. 34 (1962) 813; Brody, Moshinsky and Renero, J. Math. Phys. 6 (1965) 1540Google Scholar
  8. 8.
    Biedenharn, Giovannini and Louck, J. Math. Phys 8 (1967) 691.MathSciNetADSCrossRefGoogle Scholar
  9. 9.
    J.D. Louck and L.C. Biedenharn, J. Math. Phys. 11 (1970) 2368.MathSciNetADSMATHCrossRefGoogle Scholar
  10. 10.
    L.C. Biedenharn and J.D. Louck, J. Math. Phys. 13 (1972) 1985.MathSciNetADSMATHCrossRefGoogle Scholar
  11. 11.
    L.C. Biedenharn and J.C. Louck, Commun. Math. Phys. 8 (1968) 89MathSciNetADSCrossRefGoogle Scholar
  12. 12.
    J.D. Louck and L.C. Biedenharn, J. Math. Phys. 14 (1973) 1336.MathSciNetADSCrossRefGoogle Scholar
  13. 13.
    One of the authors (JDL) wishes to thank Professor W.H. Klink for discussions related to this point.Google Scholar
  14. 14.
    L.C. Biedenharn, M.A. Lohe and J.D. Louck, in “Group Theoretical Methods in Physics”, edited by A. Janner, T. Janssen and M. Boon ( Springer Verlag, Berlin 1976 ) p. 395.CrossRefGoogle Scholar
  15. 15.
    Operators whose eigenvalues are the individual mij are constructed in ref. 9 (cf. p. 2384)Google Scholar
  16. 16.
    It is numerically convenient to use n shift labels (for U(n) operators) even though the operator action is defined to carry SU(n) irreps into SU(n) irreps. The unimodular restriction can always be imposed on the shift labels subsequently. (This situation has an analogy in defining uni-modular weights.)Google Scholar
  17. 17.
    Extremal means that the shifts induced by the operator are a permutation of the (operator) irrep labels.Google Scholar

Copyright information

© Plenum Press, New York 1980

Authors and Affiliations

  • L. C. Biedenharn
    • 1
  • J. D. Louck
    • 2
  1. 1.Department of PhysicsDuke UniversityDurhamUSA
  2. 2.Los Alamos Scientific LaboratoryLos AlamosUSA

Personalised recommendations