Classification of Wigner Operators by a New Type of Weight Space Diagram
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.
KeywordsNull Space Tensor Operator Operator Pattern Boson Operator WIGNER Operator
Unable to display preview. Download preview PDF.
References and Footnotes
- 3.V.Bargmann and M.Moshinsky,Nucl.Phys.18(1960)697;23(1961)177.Google Scholar
- 7.M. Moshinsky, Rev. Mod. Phys. 34 (1962) 813; Brody, Moshinsky and Renero, J. Math. Phys. 6 (1965) 1540Google Scholar
- 13.One of the authors (JDL) wishes to thank Professor W.H. Klink for discussions related to this point.Google Scholar
- 15.Operators whose eigenvalues are the individual mij are constructed in ref. 9 (cf. p. 2384)Google Scholar
- 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.Extremal means that the shifts induced by the operator are a permutation of the (operator) irrep labels.Google Scholar