On renormalization of power-counting non renormalizable theories

Power-counting non-renormalizable theories should not be dismissed a priori as fundamental theories. The practical inconvenient of having infinitely many independent couplings can be faced in certain cases performing a reduction of couplings. First we study the usage of a special reduction based on the relations imposed by the renormalization group. Then, we analyze the renormalizability of a family of theories containing quantum fields interacting with a classical gravitational field and that contain a certain class of irrelevant operators. The reduction is this case is guided by a map that also indicates that these models exhibit an acausal behavior at high energies. Finally, we investigate the renormalizability of models which, although containing irrelevant operators, are renormalizable with a finite number of couplings due to the presence of Lorentz-violating kinetic term. Along this work we consider models that can violate some principle as the Lorentz symmetry or causality, but all of them preserve unitarity. The guidelines of this thesis aim to get a better understanding of the role of renormalization as classification tool, and guide the search of a generalization of the Power-Counting criterion that allows the enlargement of the set of candidate fundamental theories.