Quantization of Lorentzian 3d Gravity by Partial Gauge Fixing

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.

Notation defect fixed on pages 5 (bottom) and 6 (around Eqs. 3.1)-- 19 pages, Latex

References in corpus (4)

• Loop Quantum Gravity: An Inside View
• Quantum Gravity in 2+1 Dimensions
• A Immirzi-like parameter for 3d quantum gravity
• Application of stochastic resonance in gravitational-wave interferometer

Cited by in corpus (4)

• Faddeev-Jackiw quantization of four dimensional BF theory
• A review on geometric formulations for classical field theory: the Bonzom-Livine model for gravity
• Canonical and symplectic analysis for three dimensional gravity without dynamics
• Hamilton-Jacobi analysis for three dimensional gravity without dynamics