De anomalia de traço a renormalização: um estudo em teoria quântica de campos no espaço-tempo curvo

Abstract

This thesis investigates aspects of renormalization and conformal theories, exploring the structure of different models in curved spacetime. Initially, we analyze the renormalization of a theory of scalar electrodynamics with a massive vector field, where the mass of the vector field leads to the violation of gauge symmetry, making the Stückelberg procedure necessary. Formal arguments suggest the possible need for non-minimal linear terms in the Ricci tensor, but we show, through power counting, that such terms violate the decoupling of the longitudinal mode and, therefore, are forbidden. Using the heat-kernel technique, we calculate the divergences in one-loop and demonstrate the possibility of renormalizing the theory. From the conformal symmetry, we explore the effective action induced by anomaly in a model with a background consisting of the metric and scalar fields. In the low-energy regime, the analysis of the induced action revealed a new method for obtaining the effective potential. This technique was then applied to the Nambu-Jona-Lasinio model with torsion, considering an external gravitational field. After the bosonization of the model, we use the anomaly-induced action to determine the effective potential, which allows us to verify spontaneous symmetry breaking and derive the gap equation. Finally, we investigate the construction of generalized conformal operators in d dimensions of spacetime, from two distinct approaches. The first is based on infinitesimal conformal transformations, with the introduction of new terms through dimensional analysis. The second approach uses Wünsch’s conformal covariant derivatives for the construction of the operators.