Irreducible Cartesian Tensors. III. Clebsch-Gordan Reduction

Publisher Website
Google Scholar
Abstract
The reduction of products of irreducible Cartesian tensors is formulated generally by means of 3‐j tensors. These are special cases of the invariant mappings discussed in Part II [J. A. R. Coope and R. F. Snider, J. Math. Phys. 11, 993 (1970)]. The 3‐j formalism is first developed for a general group. Then, the 3‐j tensors and spinors for the rotation group are discussed in detail, general formulas in terms of elementary invariant tensors being given. The 6‐j and higher n‐j symbols coincide with the familiar ones. Interrelations between Cartesian and spherical tensor methods are emphasized throughout.