# Canonical quantization of non-commutative holonomies in 2 + 1 loop quantum gravity

@article{Noui2011CanonicalQO,
title={Canonical quantization of non-commutative holonomies in 2 + 1 loop quantum gravity},
author={Karim Noui and A. P{\'e}rez and Daniele Pranzetti},
journal={Journal of High Energy Physics},
year={2011},
volume={2011},
pages={1-22}
}
• Published 2 May 2011
• Physics
• Journal of High Energy Physics
In this work we investigate the canonical quantization of 2 + 1 gravity with cosmological constant Λ > 0 in the canonical framework of loop quantum gravity. The unconstrained phase space of gravity in 2 + 1 dimensions is coordinatized by an SU(2) connection A and the canonically conjugate triad field e. A natural regularization of the constraints of 2 + 1 gravity can be defined in terms of the holonomies of ${A_\pm } = A\pm \sqrt {{\Lambda e}}$. As a first step towards the quantization of…
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