FADDEEV-JACKIW QUANTIZATION OF NON-ABELIAN SYSTEMS

Abstract

The Faddeev and Jackiw procedure for the quantization of constrained gauge systems is used on the analysis of non-Abelian symmetries. The key point is that the gauge algebra of the non-Abelian constraints under generalized brackets can be reconstructed. This follows from the singular matrix that defines the basic geometric structure of the model and its corresponding zero-modes. The attainment of this algebra, not previously found in the Faddeev-Jackiw formalism for constrained theories, 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 illustrate 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.