THE ALGEBRA AND GEOMETRY OF SU(3) MATRICES

We give an elementary treatment of the defining representation and Lie algebra of the three-dimensional unitary unimodular group SU(3). The geometrical properties of the Lie algebra, which is an eight dimension al real Linear vector space, are developed in an SU(3) covariant manne r. The f and d symbols of SU(3) lead to two ways of 'multiplying' two vectors to produce a third, and several useful geometric and algebraic identities are derived. The axis-angle parametrization of SU(3) is de veloped as a generalization of that for SU(2), and the specifically ne w features are brought out. Application to the dynamics of three-level systems is outlined.