A Quantização da Gravitação em 3D com Constante Cosmológica Positiva

Abstract

It was shown by Bonzom and Livine that 2+1 gravity with cosmological constant contains an ambiguity that depends on a Barbero–Immirzi-like parameter ? known from 4D gravity. Based on this fact, we showed that, for the ? > 0 case, the Lorentzian theory can be partially reduced, thanks to a suitable gauge fixing, to a Chern–Simons theory with compact gauge group SU(2). Then we revised already known loop quantization of Chern–Simons theory for the case of a space with the topology of a cylinder. Finally we construct a quantum observable which, despite having a not trivial spectrum at the quantum level, it corresponds to a classical quantity identically null.