• Lorentz violation
• quantum field theory
• reduction of coupling
• renormalization

Power-counting non-renormalizable theories should not be dismissed a priori as fundamentaltheories. The practical inconvenient of having infinitely many independentcouplings can be faced in certain cases performing a reduction of couplings. Firstwe study the usage of a special reduction based on the relations imposed by therenormalization group. Then, we analyze the renormalizability of a family of theoriescontaining quantum fields interacting with a classical gravitational field andthat contain a certain class of irrelevant operators. The reduction is this case isguided by a map that also indicates that these models exhibit an acausal behaviorat high energies. Finally, we investigate the renormalizability of models which, althoughcontaining irrelevant operators, are renormalizable with a finite number ofcouplings due to the presence of Lorentz-violating kinetic term. Along this workwe consider models that can violate some principle as the Lorentz symmetry orcausality, but all of them preserve unitarity. The guidelines of this thesis aim toget a better understanding of the role of renormalization as classification tool, andguide the search of a generalization of the Power-Counting criterion that allows theenlargement of the set of candidate fundamental theories.