A Spinor Approach to the SU(2) Clebsch-Gordan Coefficients**Supported by the National Natural Science Foundation of China under Grant No. 11475016, and by the Scientific Research Foundation for Returned Scholars, Ministry of Education of China

Abstract

We review the irreducible representation of an angular momentum vector operator constructed in terms of spinor algebra. We generalize the idea of spinor approach to study the coupling of the eigenstates of two independent angular momentum vector operators. Utilizing the spinor algebra, we are able to develop a simple way for calculating the SU(2) Clebsch-Gordan (CG) coefficients. The explicit expression for the SU(2) CG coefficients is worked out, and some simple physical examples are presented to illustrate the spinor approach.