par Quesne, Christiane 
Référence Journal of Physics A: General Physics, 17, 4, page (791-799), 019
Publication Publié, 1984
Référence Journal of Physics A: General Physics, 17, 4, page (791-799), 019
Publication Publié, 1984
Article révisé par les pairs
| Résumé : | For pt.II see ibid., vol.17, no.4, p.777-89 (1984). Parts I and II discussed in general terms a new solution to the state labelling problem for the d-row irreducible representations (irreps) of SU(n), when reduced with respect to SO(n). This solution was termed canonical because it reflects the operation of Littlewood's branching rule for U(n) O(n) in a straightforward way. The SU(3) SO(3) case is now worked out in detail. Explicit expressions of the canonical basis states of SO(3) irreps L belonging to an SU(3) irrep (h1h 2) are obtained. The matrix of the transformation from the Bargmann-Moshinsky basis to the canonical one is also calculated. It is shown that in both cases the extra label necessary to completely specify the states can be chosen as the label js characterising an 'intermediate' SU(2) irrep in the reduction of the produce representation jL × js into SU(2) irreps j, where j = 1/2(h 1-h2) and jL = 1/2L or 1/2(L - 1) whenever h1 + h2 - L is even or odd. |
