Métodos perturbativos e não-perturbativos em teoria quântica de campos no espaço-tempo curvo

Abstract

In this thesis, we present our applications from a detailed study of promising perturba-tive and non-perturbative models in quantum field theory in curved spacetime. Initially, we employ stochastic quantization for a self-interacting nonminimal massive scalar field. Here, we study the method perturbatively through simultaneous expansions in the curva-ture tensor and in the noise fields and also nonperturbatively, i. e., without noise expan-sion. Using the Riemann normal coordinates we find the Euclidean correlation function and evaluate multi-loop quantum corrections. The stochastic correlation function repro-duces the well-known result by Bunch and Parker and is used to construct the effective potential in an arbitrary dimension D. Furthermore, we present a sample of numerical simulations for D = 3. Next, using the background field method in the approach of the nonperturbative method called functional renormalization group for the case of Yang-Mills theory, we study the background field symmetry and gauge dependence of the background average effective action, when the regulator action depends on external fields. At the end, via perturbation theory through the usual method of path integrals we study the Yukawa model with one scalar and one axial scalar fields, coupled to N copies of Dirac fermions, in curved spacetime background. From the the heat-kernel technique, we derive the one-loop divergences, describe the renormalization of the theory and calculate the full set of beta-and gamma-functions for all coupling constants and fields. We obtain the contribution of scalar fields to the 1-loop effective potential and discuss some difficulties of the renorma-lization group approach to the effective potential in the model under consideration. Keywords: Nonperturbative methods, stochastic quantization, semiclassical gravity, functional renormalization group, background field formalism, Yukawa model, curved spa-cetime.