SU(4)⊃SU(2)⊗SU(2) Projection Techniques

Abstract

The twofold multiplicity problem associated with the Wigner supermultiplet reduction SU(4)⊃SU(2)⊗SU(2)SU(4)⊃SU(2)⊗SU(2) is resolved by spin‐isospin projection techniques analogous to the angular momentum projection technique introduced by Elliott to resolve the SU(3)⊃R(3)SU(3)⊃R(3) multiplicity problem. The projection quantum numbers, which furnish either an integer or half‐integer characterization of the multiplicity, are assigned according to an (ST)‐multiplicity formula derived from a consideration of the symmetry properties of spin‐isospin degeneracy diagrams. An expression is obtained for the coefficients which relate the SU(4)⊃SU(2)⊗SU(2)SU(4)⊃SU(2)⊗SU(2) projected basis states to states labeled according to the natural U(4)⊃U(3)⊃U(2)⊃U(1)U(4)⊃U(3)⊃U(2)⊃U(1) chain. General expressions for SU(4)⊃SU(2)⊗SU(2)SU(4)⊃SU(2)⊗SU(2) coupling coefficients and tensorial matrix elements are given in terms of the corresponding U(4)⊃U(3)⊃U(2)⊃U(1)U(4)⊃U(3)⊃U(2)⊃U(1) quantities