1204.5455 (Rodrigo M S Barbosa et al.)

Quantization of Lorentzian 3d Gravity by Partial Gauge Fixing    [PDF]

Rodrigo M S Barbosa, Clisthenis P Constantinidis, Zui Oporto, Olivier Piguet

D = 2+1 gravity with a cosmological constant has been shown by Bonzom and Livine to present a Barbero-Immirzi like ambiguity depending on a parameter. We make use of this fact to show that, for positive cosmological constant, the Lorentzian theory can be partially gauge fixed and reduced to an SU(2) Chern-Simons theory. We then review the already known quantization of the latter in the framework of Loop Quantization for the case of space being topogically a cylinder. We finally construct, in the same setting, a quantum observable which, although non-trivial at the quantum level, corresponds to a null classical quantity.

View original: http://arxiv.org/abs/1204.5455