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arXiv · 1101.5585

2+1 gravity with positive cosmological constant in LQG: a proposal for the physical state

Daniele Pranzetti
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Abstract

In this paper, I investigate the possible quantization, in the context of LQG, of three dimensional gravity in the case of positive cosmological constant Λ and try to make contact with alternative quantization approaches already existing in the literature. Due to the appearance of an anomaly in the constraints algebra, previously studied as a first step of the analysis, alternative techniques developed for the quantization of systems with constraints algebras not associated with a structure Lie group need to be adopted. Therefore, I introduce an ansatz for a physical state which gives some transition amplitudes in agreement with what one would expect from the Turaev-Viro model. Moreover, in order to check that this state implements the right dynamicss, I show that it annihilates the master constraint for the theory up to the first order in Λ.

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Daniele Pranzetti. 2011-10-10. 2+1 gravity with positive cosmological constant in LQG: a proposal for the physical state. https://doi.org/10.1088/0264-9381%2F28%2F22%2F225025

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