An improved Gauge Unfixing formalism and the Abelian Pure Chern Simons Theory

We propose a variant scheme of the Gauge Unfixing formalism which modifies directly the original phase space variables of a constrained system. These new variables are gauge invariant quantities. We apply our procedure in a mixed constrained system that is the Abelian Pure Chern Simons Theory where several gains are obtained. In particular, from the gauge invariant Hamiltonian and using the inverse Legendre transformation, we obtain the same initial Abelian Pure Chern Simons Lagrangian as the gauge invariant Lagrangian. This result shows that the gauge symmetry of the action is certainly preserved.Comment: revised version. To appear in Brazilian Journal of Physic

Removing the Wess Zumino fields in the BFFT formalism

In this paper we give some prescriptions in order to remove the Wess Zumino fields of the BFFT formalism and, consequently, we derive a gauge invariant system written only in terms of the original second class phase space variables. Here, the Wess Zumino fields are considered only as auxiliary variables that permit us to reveal the underlying symmetries present in a second class system. We apply our formalism in three important and illustrative constrained systems which are the Chern Simons Proca theory, the Abelian Proca model and the reduced SU(2) Skyrme model.Comment: revised versio