We propose a new procedure to embed second class systems by introducing Wess-Zumino (WZ) fields in order to unveil hidden symmetries existent in the models. This formalism is based on the direct imposition that the new Hamiltonian must be invariant by gauge-symmetry transformations. An interesting feature in this approach is the possibility to find a representation for the WZ fields in a convenient way, which leads to preserve the gauge symmetry in the original phase space. Consequently, the gauge-invariant Hamiltonian can be written only in terms of the original phase-space variables. In this situation, the WZ variables are only auxiliary tools that permit to reveal the hidden symmetries present in the original second class model. We apply this formalism to important physical models: the reduced-SU(2) Skyrme model, the Chern-Simons-Proca quantum mechanics and the chiral bosons field theory. In all these systems, the gauge-invariant Hamiltonians are derived in a very simple way.

Revised version. Title changed for Gauging by symmetries. To appear in IJMPA