Finite Transformations of <i>SU</i>3

Abstract

The properties of SU3 finite transformations are investigated. These transformations on the defining three-dimensional complex space are parameterized in a form employing three factors, two of which are the Euler parameterization of an SU2 subgroup. The irreducible representations of the factored parameterization are found explicitly. The volume element is calculated and the orthogonality relation is verified. Spherical harmonic basis states are derived as a specialization of the transformation matrix. Another result is a definition of triality and a simple proof that it is additive modulus three.