Traces of products of components of angular momentum operators

M. E. Rose

The angular momentum operators define a set of irreducible tensors which are unique except for a normalization constant. The normalization is conveniently defined in terms of statistical tensors which describe oriented states. The properties of the tensors discussed here include: (1) the trace of products of components of such tensors, (2) symmetry properties of the traces, and (3) the expansion of products of components of these tensors into a sum of irreducible tensors. The corresponding expansion of commutators and anticommutators of these components is also discussed briefly.

Naeem Ullah

The products of exponentials containing various angular momentum operators are expressed on a single rotation operator. This gives new expressions for the traces of products of angular momentum operators in terms of hypergeometric functions. Since hypergeometric functions are related to Jacobi polynomials, the traces can also be expressed in terms of these polynomials.

H. E. De Meyer, Guido Vanden Berghe

Analytic expressions are derived for the traces of products of angular momentum operators in the spherical basis. These expressions contain binomial coefficients and Stirling numbers of the second kind. In addition, some relations between Bernouilli polynomials and Stirling numbers are retrieved.