  In this thesis we present the application of the \textit{abelian color cycle}
(ACC) and the \textit{abelian color flux} (ACF) methods to several models: the
SU(2) principal chiral model, the SU(2) gauge theory with staggered fermions
and QCD with staggered fermions. The key step of our approaches consists in
decomposing the action of the model one is considering into its minimal units.
For gauge theories those minimal terms are complex numbers, which we refer to
as abelian color cycles, while for fermions the action is decomposed into
Grassmann bilinears, which we called abelian color fluxes. As a result of these
decompositions the actions are sums of commuting terms, and thus one can
proceed with the dualization of the theory as in the abelian case, by
factorizing and expanding the Boltzmann weight. The expansion indices,
so-called dual variables, become the new degrees of freedom for the description
of the system once the conventional fields are integrated out. The integration
over the conventional fields results into weight factors and constraints. The
constraints implement the symmetries of the theory in the dual form and imply
that the dual configurations which contribute to the long range physics are
worldsheets for the gauge degrees of freedom and worldlines for matter fields.
On the other hand, the weight factors allow one to organize the dual partition
function into a strong coupling series of which all terms are known in closed
form. Moreover, the form of the dependence on the chemical potential allows one
to identify the net-particle number as the total net temporal winding number of
the worldlines in the dual representation.
