Traces of Products of Angular Momentum Matrices

Closed formulas are given for evaluating $\mathrm{Tr}{\mathrm{\hspace{0.17em}J}}_a^p{J}_b^q{J}_c^r\cdots$ where a, b, c, ⋯ are equal to x, y, or z and p, q, r, ⋯ are non‐negative integers for which p+q+r+ ⋯ ≤ 10. All possible combinations of the angular momentum components for p+q+r+ ⋯ ≤ 9 are included. Numerical values of the traces are given for J = ½, 1, ⋯ 10. The procedures used in evaluating the traces are described.