O grupo de renormalização em modelos de gravitação

Abstract

On this thesis, we explored differents aspects of the renormalization group (RG) in Quantum Gravity. Specifically, we studied the RG applied to three differents models. We began studying the RG on-shell and we used for that the model of gravity with torsion proposed by Cartan, we made the quantum treatment of this theory. Then, we showed in details the calculations of the study of semi-classical theory, using for that, the method of physical renormalization, based on the momentum subtraction. On this part, we gave the details of the derivation of gravitational form factors, using the method of the heat kernel for three massive theories: scalar field, vector field and fermionic field which leads us to the gravitational analogue of the decoupling theorem from Appelquist and Carazzone. In this part, we just remade the calculations already undertaken in a paper by Gorbar and Shapiro, but now in minute details for each step calculated. On the last part, an analysis of the functional renormalization group (FRG) was made, applying this technique also to the model of semiclassical gravity, where the theory addressed was a theory with a scalar field with non-minimal coupling in curved spacetime.