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A solution to the SU(n) external state labelling problem based upon a U(n-1, n-1) group. II. Recursion relations for the SU(2) and SU(3) Wigner coefficients

par Quesne, Christiane
Référence Journal of Physics A: Mathematical and General, 20, 9, page (2259-2278), 015
Publication Publié, 1987

Article révisé par les pairs

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Résumé :

The new solution to the SU(n) external state labelling problem, proposed in the first paper of this series, is analysed in detail in the SU(3) case in terms of the two complementary chains U(3)*U(3) contains/implies U(3) and U(2, 2) contains/implies U(2)*U(2). The classification of SU(3) coupled states is completed by the labels of an intermediate U(2) irreducible representation hs=(hs1hs2), directly related to King's branching rule for U( 3)*U(3)U(3). For pedagogical purposes, the SU(2) coupled state construction, based upon the complementary chains U(2)*U(2) contains/implies U(2) and U(1, 1) contains/implies U(1)*U(1), is considered first. For both SU(2) and SU(3), it is proved that, in addition to the standard recursion relations, the corresponding Wigner coefficients satisfy recursion relations of a different type, arising from the action of the U(1, 1) or U(2, 2) complementary group generators. A detailed example shows that such complementary recursion relations are quite useful for numerical purposes.