Teorias de campo efetivas no espaço tempo curvo

Abstract

In this thesis we apply the effective approach in order to derive the quantum contributions to gravitation induced by the quantization of the fields of matter. We present a study of the form factors in a simplified gravity model in 2D for the scalar, spinor and massive vector fields using the heat kernel solution presented by Codello & Zanusso. In this study, the simplicity of the model allows us to clearly explore the ultraviolet (UV) regime of the results that lead us to the usual action of Polyakov in the conformal case, while generalizing the form of this action in the case of a non-minimal scalar field. The infrared (IR) limit is also explored, which leads us to the decoupling theorem both from form factors and beta functions. Finally, we explored in detail the construction of an effective theory of low energies for a model of light scalar fields coupled to a scalar field of much larger mass. Our main interest is to show that even in the curved space-time the heavy field decouples in the IR, and the results for the diagrams with mixed internal lines can be described by an effective theory that takes into account only the light fields.