ISSN:
1089-7658
Quelle:
AIP Digital Archive
Thema:
Mathematik
,
Physik
Notizen:
Minimal biorthogonal systems of the Clebsch–Gordan (Wigner) coefficients of SU(3)&supuline;U(2) are discussed as well as the dual coupled bases. The closed system of analytical expressions for the dual isofactors (reduced Wigner coefficients) and the overlaps of coupled states is obtained with the help of analytical inversion symmetry. The Regge-type symmetry of the overlaps and the boundary orthonormal isofactors (orthogonalization coefficients) is discovered. The polynomial structure of the alternative complete algebraic systems of the orthonormal SU(3) isofactors (characterized by the null spaces, symmetries, and additional selection rules and obtained by means of the Hecht or Gram–Schmidt process) is considered. The realizations of the external "missing label'' operators of the third and the fourth orders in the minimal coupled bases, which lead to preferable algorithms to evaluate the orthonormal SU(3) coupling coefficients satisfying different symmetry properties, are presented. With the help of the 6j coefficients of SU(2) or inverted truncated SU(2) recoupling matrices, the biorthogonal systems associated with the SU(3) canonical tensor operators are expanded in terms of minimal ones.
Materialart:
Digitale Medien
URL:
http://dx.doi.org/10.1063/1.528119
