Angular Momentum Theory

Abstract

Angular momentum theory is presented from the viewpoint of the group SU(1) of unimodular unitary matrices of order two. 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 1n-j coefficients, with an almost boundless set of inter-relations, and presentations of the associated conceptual framework. The relationship to the rotation group in physical 3-space 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 inter-relate the material to the special functions of mathematics and to the combinatorial foundations of the subject.