SU3 isoscalar factors

Abstract

A summary of the properties of the Wigner Clebsch-Gordan coefficients and isoscalar factors for the group SU3 in the SU2$\otimes$U1 decomposition is presented. The outer degeneracy problem is discussed in detail with a proof of a conjecture (Braunschweig's) which has been the basis of previous work on the SU3 coupling coefficients. Recursion relations obeyed by the SU3 isoscalar factors are produced, along with an algorithm which allows numerical determination of the factors from the recursion relations. The algorithm produces isoscalar factors which share all the symmetry properties under permutation of states and conjugation which are familiar from the SU2 case. The full set of symmetry properties for the SU3 Wigner-Clebsch-Gordan coefficients and isoscalar factors are displayed.

20 pages, LaTeX (earlier version incomplete)

Cited by in corpus (3)

• Program for Generating Tables of SU(3) Coupling Coefficients
• A complementary group technique for the resolution of the outer multiplicity problem of SU(n): (II) A recoupling approach to the solution of SU(3)\supset U(2) reduced Wigner coefficients
• A complementary group technique for a resolution of the outer multiplicity problem of SU(n): (I) Littlewood rule and a complementary group of SU(n)