Complete loop quantization of a dimension 1+2 Lorentzian gravity theory

Abstract

De Sitter Chern-Simons gravity in D = 1 + 2 spacetime is known to possess an extension with a Barbero-Immirzi like parameter. We find a partial gauge fixing which leaves a compact residual gauge group, namely SU(2). The compacticity of the residual gauge group opens the way to the usual LQG quantization techniques. We recall the exemple of the LQG quantization of SU(2) CS theory with cylindrical space topology, which thus provides a complete LQG of a Lorentzian gravity model in 3-dimensional space-time.

arXiv commentLoops11 - Madrid - 2011 (4 pages, Latex)

References in corpus (13)

• Background Independent Quantum Gravity: A Status Report
• Real Ashtekar Variables for Lorentzian Signature Space-times
• Barbero's Hamiltonian derived from a generalized Hilbert-Palatini action
• Real and complex connections for canonical gravity
• Fundamental Structure of Loop Quantum Gravity
• Loop quantum gravity: an outside view
• Loop Quantum Gravity: An Inside View
• Reality Conditions and Ashtekar Variables: a Different Perspective
• Quantum Gravity in 2+1 Dimensions
• New Variables for Classical and Quantum Gravity in all Dimensions II. Lagrangian Analysis
• A Immirzi-like parameter for 3d quantum gravity
• The Hilbert space of Chern-Simons theory on the cylinder. A Loop Quantum Gravity approach
• Application of stochastic resonance in gravitational-wave interferometer