6-j symbol

Summary

The Wigner 6-j symbol $\begin{Bmatrix} j_1 & j_2 & j_3 \\ j_4 & j_5 & j_6 \end{Bmatrix}$ is a number attached to six spins. It compares the two ways to couple three irreducible representations of SU(2): first the first two, or first the last two. It is a sum of products of four 3-j symbols, and it is closely related to the Racah W-coefficient and to the Racah polynomials. 6-j symbols are used in atomic and nuclear physics, and in the construction of invariants of 3-manifolds.