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}
}
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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References

SHOWING 1-10 OF 53 REFERENCES
On the regularization of the constraint algebra of quantum gravity in 2 + 1 dimensions with a nonvanishing cosmological constant
We use the mathematical framework of loop quantum gravity (LQG) to study the quantization of three-dimensional (Riemannian) gravity with a positive cosmological constant (Λ > 0). We show that the
Uniqueness of Diffeomorphism Invariant States on Holonomy–Flux Algebras
Loop quantum gravity is an approach to quantum gravity that starts from the Hamiltonian formulation in terms of a connection and its canonical conjugate. Quantization proceeds in the spirit of Dirac:
Modern Canonical Quantum General Relativity
The open problem of constructing a consistent and experimentally tested quantum theory of the gravitational field has its place at the heart of fundamental physics. The main approaches can be roughly
Three-dimensional loop quantum gravity: physical scalar product and spin-foam models
In this paper, we address the problem of the dynamics in three-dimensional loop quantum gravity with zero cosmological constant. We construct a rigorous definition of Rovelli's generalized projection
The spin-foam-representation of loop quantum gravity
The problem of background independent quantum gravity is the problem of defining a quantum field theory of matter and gravity in the absence of an underlying background geometry. Loop quantum gravity
Hamiltonian Quantization of Chern-Simons theory with SL(2,C) Group
We analyze the hamiltonian quantization of Chern-Simons theory associated to the real group SL(2,C)R, universal covering of the Lorentz group SO(3, 1). The algebra of observables is generated by
Hamiltonian quantization of Chern-Simons theory with SL(2, Bbb C) group
We analyse the Hamiltonian quantization of Chern–Simons theory associated with the real group SL(2, ), universal covering group of the Lorentz group SO(3, 1). The algebra of observables is generated
Noncommutative harmonic analysis, sampling theory and the Duflo map in 2+1 quantum gravity
We show that the ⋆-product for U(su2), group Fourier transform and effective action arising in Freidel and Livine (2005 Preprint hep-th/0502106) in an effective theory for the integer spin
2 + 1 gravity with a positive cosmological constant in LQG: a proposal for the physical state
In this paper, I investigate the possible quantization, in the context of loop quantum gravity, of three-dimensional gravity in the case of positive cosmological constant Λ and try to make contact
The Hamiltonian constraint in 3d Riemannian loop quantum gravity
We discretize the Hamiltonian scalar constraint of three-dimensional Riemannian gravity on a graph of the loop quantum gravity phase space. This Hamiltonian has a clear interpretation in terms of
...
...