The Clebsch-Gordan coefficients of SU(3) and the orthogonalization problem

Abstract

The Clebsch-Gordan coefficients of the group SU(3) are determined by integrating the product of three matrix elements of finite transformations belonging to three irreducible representations of the group. Compact expressions involving a single or a double sum over products of 3-j and 6-j symbols of SU(2) are obtained for several different classes of coefficients by suitably restricting the initial states but keeping the final states of the matrix elements arbitrary. To orthogonalize the CG coefficients, a linear combination of several integrals with the same final but different initial states is taken. The coefficients of the linear combination are determined by the Schmidt procedure and are found to be expressible in terms of integrals of the same type.