Wigner and Racah coefficients for SU3

Abstract

A general yet simple and hence practical algorithm for calculating SV, ::l SV 2 X V, Wigner coefficients is formulated. The resolution of the outer multiplicity follows the prescription given by Biedenharn and Louck. Ii is shown that SV 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 SV3 ::l SV2 X VI Wigner coefficient construction algorithm. A general expression for evaluating SV3 ::l R3 Wigner coefficients as a sum over a simple subset of the corresponding SU 3 ::l SV 2 X VI Wigner coefficients is also presented. State conjugation properties are discussed and symmetry relations for both the SV3::l SV 2 X VI and SV 3 ::l R3 Wigner coefficients are given. Machine codes based on the results are available.

Transition probabilities in the U(3,3) limit of the symplectic interacting vector boson model

“…and the phase convention is chosen to agree with that of Draayer and Akiyama [28]. For ρ = 2 we have (λ, µ)|||A ′20…”

“…With the help of the above analytic expressions (36), (38) and (39) for the matrix elements of the tensor operators forming the E2 transition operator we can calculate the transition probabilities (33) between the states of the ground state band as attributed to the SU * (3) symmetry-adapted basis states of the model (25). All the required U (3) IF's are numerically obtained using the computer code [28].…”

“…(29) and (32) are not known in general. A computer code is available for their numerical evaluation [28].…”

Structure and decay width of the in a one-gluon exchange model

“…Possible sets of (Γ 12 , Γ 34 , Γ 1234 ) in the diquark model are listed in Table III. The transformation between the diquark coupling and the successive coupling can be performed using the formula (17) (by replacing the Racah coefficient with the corresponding one in the SU(3) algebra [28,29]). Here the angular momentum label J should be understood to denote the color SU(3) label Γ.…”

Schematic model for QCD at finite temperature

“…The index σ represents the two spin components ± 1 2 , the index i = 1 or 2, stands for the upper or lower level and the index α represents all remaining degrees of freedom, which are at least 3 if the color degree of freedom is considered. Lowering and raising the indices of the operators introduces a phase, which depends on the convention used [13], and a change of the indices to their conjugate values, i.e., the quantum numbers (1, 0)Y T T z σ change to (0, 1) − Y T − T z − σ.…”