Gravitação quântica canônica

Abstract

In this work, one presents the canonical formalism for quantizing gravity, both in its original formulation, for which the metric is the canonical variable, and in Ashtekar’s formalism, where the self-dual connection plays the role of the canonical variable. In this last formulation, the constraint equations of the formalism are drastically simplified, and, making use of Chern-Simons theory, one builds a state which satisfies these equations in the vacuum, constituting an important solution for the Wheeler-DeWitt equation. The Chern-Simons state also has a loop representation, which receives this name because it’s formulated in terms of Wilson loops.