Faddeev-Jackiw approach to gauge theories and ineffective constraints

Abstract

The general conditions for the applicability of the Faddeev-Jackiw approach to gauge theories are studied. When the constraints are effective a new proof in the Lagrangian framework of the equivalence between this method and the Dirac approach is given. We find, however, that the two methods may give different descriptions for the reduced phase space when ineffective constraints are present. In some cases the Faddeev-Jackiw approach may lose some constraints or some equations of motion. We believe that this inequivalence can be related to the failure of the Dirac conjecture (that says that the Dirac Hamiltonian can be enlarged to an Extended Hamiltonian including all first class constraints, without changes in the dynamics) and we suggest that when the Dirac conjecture fails the Faddeev-Jackiw approach fails to give the correct dynamics. Finally we present some examples that illustrate this inequivalence.