Restoring Gauge Invariance in Non-Abelian Second-class Theories

In this paper, we propose a generalization of the improved gauge unfixing formalism in order to generate gauge symmetries in the non-Abelian valued systems. This generalization displays a proper and formal reformulation of second-class systems within the phase space itself. Then, we present our formalism in a manifestly gauge invariant resolution of the SU(N) massive Yang-Mills and SU(2) Skyrme models, where gauge invariant variables are derived.