New realizations of the dual space of SU(3)

The logic of constructing and interrelating classical realizations of the dual space of SO(3) is exhibited. Analogies with different methods of quantization of gauge theories are pointed out. The analysis is applied to SU(3) to obtain existing realizations and to construct new ones. The Gelfand-Zetlyn basis for the irreducible representations of SU(3) is explicitly realized using polynomials in four variables and positive or negative integral powers of a fifth variable. Another realization uses a spinor of SO(6)*SO(3,1). These are the analogues of Schwinger-Bargmann construction for SU(2).