Wigner and Racah coefficients for SU3

Abstract

A general yet simple and hence practical algorithm for calculating SU 3 ⊃SU 2 ×U 1 Wigner coefficients is formulated. The resolution of the outer multiplicity follows the prescription given by Biedenharn and Louck. It is shown that SU 3 Racah coefficients can be obtained as a solution to a set of simultaneous equations with unknown coefficients given as a by‐product of the initial steps in the SU 3 ⊃SU 2 ×U 1 Wigner coefficient construction algorithm. A general expression for evaluating SU 3 ⊃R 3 Wigner coefficients as a sum over a simple subset of the corresponding SU 3 ⊃SU 2 ×U 1 Wigner coefficients is also presented. State conjugation properties are discussed and symmetry relations for both the SU 3 ⊃SU 2 ×U 1 and SU 3 ⊃R 3 Wigner coefficients are given. Machine codes based on the results are available.