Loop Quantization of a Model for D=1+2 (Anti)de Sitter Gravity Coupled to Topological Matter

Abstract

We present a complete quantization of Lorentzian D=1+2 gravity with cosmological constant, coupled to a set of topological matter fields. The approach of Loop Quantum Gravity is used thanks to a partial gauge fixing leaving a residual gauge invariance under a compact semi-simple gauge group, namely Spin(4) = SU(2) x SU(2). A pair of quantum observables is constructed, which are non-trivial despite of being null at the classical level.

18 pages, Latex. Two references added

References in corpus (2)

• A Immirzi-like parameter for 3d quantum gravity
• A note on the Holst action, the time gauge, and the Barbero-Immirzi parameter

Cited by in corpus (1)

• Thermodynamical and dynamical stability of Einstein-Maxwell and extremal Einstein-Born-Infeld thin shells in $(2+1)$ dimensions