  The concept of gauge invariance can be considered one of the most subtle and
useful concept in theoretical physics since it can permit the comprehension of
difficult systems in physics with an arbitrary choice of a reference frame at
every instant of time. It is always desirable to have a bridge between gauge
invariant and noninvariant theories. Once established, this kind of mapping
between first-class (gauge invariant) and second-class systems, in Dirac's
formalism can be considered as a sort of duality. In this paper we investigate
this "duality" obtaining a gauge invariant theory starting with a noninvariant
one. We analyzed both Abelian and non-Abelian theories and the procedure used
is the recent dual (also called symplectic) embedding formalism. We believe
that this method is the most convenient one since it is not plagued by the
ambiguity problems that torments BFFT and other iterative methods. We
demonstrated exactly that this "dualization" method used here does not require
any special modification to handle with non-Abelian systems, which is also a
new result described in this paper. To prove the gauge invariance we used just
the Dirac constraint technique. It is relevant to say here that, although this
work is lengthy, the majority of the results presented here are new in the
literature. The results that are not new were reproduced within a new
perspective.
