ON THE DEGENERACY PROBLEM IN SU(3)

Abstract

The recent suggestion of Macfarlane, O'Raifeartaigh, and Rao that mixed Casimir operators be used to resolve the external degeneracy problem is applied to the group SU(3). The significant operator is the part of the cubic mixed Casimir operator which is antisymmetric with respect to the two factor spaces and also with respect to starred and unstarred variables. The matrix of this operator is derived with respect to a convenient set of functions and is found to have a simple form. The eigenfunctions are simply related to the usual symmetric and antisymmetric functions in the case of degeneracy 2 with equal factor representations.