On the Euler angles for the classical groups, Schwinger approach and Isoscalar factors for SU (3)

TL;DR

This paper develops recurrence formulas and generating functions for classical groups, especially SU(3), introducing new bases and methods to compute isoscalar factors and representation matrix elements.

Contribution

It generalizes Euler angles and invariant measures for classical groups, introduces a new basis for SU(3), and provides a method to calculate isoscalar factors and matrix elements.

Findings

Derived recurrence formulas for classical groups

Introduced a new basis for SU(3) eigenfunctions

Provided generating functions and analytical expressions for SU(3) elements

Abstract

We establish recurrences formulas of the order of the classical groups that allow us to find a generalization of Euler's angles for classical groups and the invariant measures of these groups. We find the generating function for the SU(2) subset of SU(3) basis in the Fock-Bargmann space and a new basis of SU(3). This new basis is eigenfunction of the square of kinetic moment in product spaces of spherical harmonics. We generalize the generating function of SU (2) and we find invariant polynomials of SU (3) which are elements of the basis of SU (6). Using the above results we deduce the method of calculation isoscalar factors. We expose this method and we give the generating function for a particular case. Finally we determine the generating function of the elements of the representation matrix of SU(3) and we derive the analytical expression of these elements.