Abstract and subjects
Angular momentum theory is presented from the viewpoint of the group SU(1) of unimodular unitary matrices of order 2. This is the basic quantum mechanical rotation group for implementing the consequences of rotational symmetry into isolated complex physical systems and gives the structure of the angular momentum multiplets of such systems. This entails the study of representation functions of SU(2), the Lie algebra of SU(2) and copies thereof, and the associated Wigner–Clebsch–Gordan coefficients, Racah coefficients, and 3n − j coefficients, with an almost boundless set of interrelations, and presentations of the associated conceptual framework. The relationship of SU(2) to the rotation group in physical 3-space R3 is given in detail. Formulas are often given in a compendium format with brief introductions on their physical and mathematical content. A special effort is made to interrelate the material to the special functions of mathematics and to the combinatorial foundations of the subject.