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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: theSU(2) principal chiral model, the SU(2) gauge theory with staggered fermionsand QCD with staggered fermions. The key step of our approaches consists indecomposing the action of the model one is considering into its minimal units.For gauge theories those minimal terms are complex numbers, which we refer toas abelian color cycles, while for fermions the action is decomposed intoGrassmann bilinears, which we called abelian color fluxes. As a result of thesedecompositions the actions are sums of commuting terms, and thus one canproceed with the dualization of the theory as in the abelian case, byfactorizing and expanding the Boltzmann weight. The expansion indices,so-called dual variables, become the new degrees of freedom for the descriptionof the system once the conventional fields are integrated out. The integrationover the conventional fields results into weight factors and constraints. Theconstraints implement the symmetries of the theory in the dual form and implythat the dual configurations which contribute to the long range physics areworldsheets for the gauge degrees of freedom and worldlines for matter fields.On the other hand, the weight factors allow one to organize the dual partitionfunction into a strong coupling series of which all terms are known in closedform. Moreover, the form of the dependence on the chemical potential allows oneto identify the net-particle number as the total net temporal winding number ofthe worldlines in the dual representation.

Abelian color cycle and abelian color flux dualization methods for non-abelian lattice field theories