SYMPLECTIC QUANTIZATION OF CONSTRAINED SYSTEMS

It is shown that the symplectic two-form, which defines the geometrical structure of a constrained theory in the Faddeev-Jackiw approach, may be brought into a non-degenerated form, by an iterative implementation of the existing constraints. The resulting generalized brackets coincide with those obtained by the Dirac bracket approach, if the constrained system under investigation presents only second-class constraints. For gauge theories, a symmetry breaking term must be supplemented to bring the symplectic form into a non-singular configuration. At present, the singular symplectic two-form provides directly the generators of the time independent gauge transformations.