FADDEEV-JACKIW QUANTIZATION OF NON-ABELIAN SYSTEMS

The Faddeev and Jackiw procedure for the quantization of constrained g auge systems is used on the analysis of non-Abelian symmetries. The ke y point is that the gauge algebra of the non-Abelian constraints under generalized brackets can be reconstructed. This follows from the sing ular matrix that defines the basic geometric structure of the model an d its corresponding zero-modes. The attainment of this algebra, not pr eviously found in the Faddeev-Jackiw formalism for constrained theorie s, leads to the correct transformation properties for the gauge fields . This construction shows that the zero-modes of the symplectic matrix and the generators of gauge symmetry are closely related. To illustra te the method studied here we consider a simple mechanical model with an underlying non-Abelian symmetry and the field theory of pure Chern- Simons theory in (2 + 1) dimensions.