Loop quantization of a model for D = 1 + 2 (anti)de Sitter gravity coupled to topological matter

Author: Constantinidis Clisthenis P   Oporto Zui   Piguet Olivier  

Publisher: IOP Publishing

E-ISSN: 1361-6382|32|5|55007-55027

ISSN: 0264-9381

Source: Classical and Quantum Gravity, Vol.32, Iss.5, 2015-03, pp. : 55007-55027

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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) × SU(2). A pair of quantum observables is constructed, which are non-trivial despite being gauge-equivalent to zero at the classical level. A semi-classical approximation based on appropriately defined coherent states shows non-vanishing expectation values for them, thus not reproducing their classical behaviour.