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arXiv · 1204.5455

Quantization of Lorentzian 3d Gravity by Partial Gauge Fixing

Rodrigo M. S. Barbosa·Clisthenis P Constantinidis·Zui Oporto·Olivier Piguet
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Abstract

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.

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Rodrigo M. S. Barbosa, Clisthenis P Constantinidis, Zui Oporto, Olivier Piguet. 2012-04-30. Quantization of Lorentzian 3d Gravity by Partial Gauge Fixing. https://doi.org/10.1088/0264-9381%2F29%2F15%2F155011

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