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

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.

17 pages; minor changes, presentation improved. Version accepted for publication in CQG

References in corpus (2)

• Canonical quantization of non-commutative holonomies in 2+1 loop quantum gravity
• Chern-Simons theory, Stokes' Theorem, and the Duflo map

Cited by in corpus (6)

• Symmetries of quantum space-time in 3 dimensions
• Geometric temperature and entropy of quantum isolated horizons
• Statistical Entropy of a BTZ Black Hole from Loop Quantum Gravity
• Turaev-Viro amplitudes from 2+1 Loop Quantum Gravity
• Dynamical evaporation of quantum horizons
• Non-commutative holonomies in 2+1 LQG and Kauffman's brackets