Análise canônica da teoria gravitacional

Abstract

There is no consistent quantum description for the gravitational field. There is a significant number of models that seek such a description, where one of the means by which one can quantize a theory is through canonical quantization or functional integrals of Feynmann. In this project, we seek to study the necessary tools for the classical description of the Hamiltonian of General Relativity (GR), which is fundamental in future canonical quantization. In order to describe the Hamiltonian of General Relativity it is necessary to foliation space-time M using the ADM formalism. And furthermore a systematic analysis of the boundary terms present in the gravitational action is necessary, they represent energy in the Hamiltonian description, lead to a good behavior of the Hamiltonian variation. Like most classical theories, RG has in its Hamiltonian description the presence of constraints due to its structure of symmetry: invariance of diffeomorphisms. We will explore in detail the canonical structure of GR. In view of this construction its application in alternative models was also made. Here we apply in a unimodular theory that mathematically consists of an imposition on the metric tensor making it constant. In addition, in the field equations of the unimodular theory, the cosmological constant appears as a constant of integration, without the need to couple it to the gravitational field. It has been shown that classically the unimodular theory is consistent with the canonical analysis of the GR. In a future work, the know how acquired with the study of GR Hamiltonian formulation and its application to alternative models will provide sufficient conditions to delve into some model or theory for quantum gravity.