Wigner coefficients of U(4) ⊃ SUS(2) ⊗ SUT(2)

Abstract

The Wigner coefficients of U(4)⊃SUS(2) ⊗SUT(2) for the coupling [n14,n24,n34,n44]⊗[n14′,n24′,n34′,n44′]↓[n14″,n24″,n34″,n44″] with arbitrary irreducible representations [n14,n24,n34,n44] and [n14′,n24′,n34′,n44′] of U(4) are derived with an expression involving the Wigner coefficients of U(4) in the canonical U(4)⊃U(3)⊃U(2) ⊃U(1) basis and the state expansion coefficients of U(4)⊃SUS(2)⊗SUT(2) in terms of those of the U(4) canonical basis determined previously. Algebraic expressions of the elementary Wigner coefficients of U(4)⊃SUS(2)⊗SUT(2) in terms of the state expansion coefficients are explicitly provided.