Calculation of the Clebsch--Gordan coefficients and their physical application

Questions on the theory of Clebsch-Gordan coefficients are discussed from the viewpoint of their physical application. The apparatus of the generalized theory of angular momentum including both the Regge symmetry and higher symmetries is constracted. The relation of the theory of angular momentum with the topological properties of multidimensional spaces is examined. Calculation techniques are developed for the ClebschGordan coefficients of the Lee compact group, preferentially the SU/sub n/ group, closely connected with the generalized theory of angular momentum. On the basis of the theory of Clebsch- Gordan coefficients a method is proposed for the calculation of the relativistic cross section. A method of group analysis of complex physical systems (atoms, nuclei, molecules, elementary particles, and radiation) is also developed. A series of practical results is obtained. Special attention is given to the aspects of universality of the Clebsch-Gordan coefficients and to the investigation of their interaction with various areas of mathematics and physics. (tr-auth)