Faddeev-Jackiw quantization of non-abelian systems

H. MONTANI; C. WOTZASEK

MODERN PHYSICS LETTERS A

WORLD SCIENTIFIC PUBL CO PTE LTD

Lugar: London, UK; Año: 1993 vol. 8 p. 3387 - 3396

0217-7323

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 disclose a deep connection between the zero-modes of the sympletic matrix and the generators of gauge symmetry. To illustrated 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.