2+1 Quantum Gravity with Barbero-Immirzi like parameter on Toric Spatial Foliation

Abstract

We consider gravity in 2+1 space-time dimensions, with negative cosmological constant and a `Barbero-Immirzi' (B-I) like parameter, when the space-time topology is of the form $ T^2 \times \mathbbm{R}$. The phase space structure, both in covariant and canonical framework is analyzed. Full quantization of the theory in the 'constrain first' approach reveals a finite dimensional physical Hilbert space. An explicit construction of wave functions is presented. The dimension of the Hilbert space is found to depend on the `Barbero-Immirzi' like parameter in an interesting fashion. Comparative study of this parameter in light of some of the recent findings in literarure for similar theories is presented.

Latex, Substantial changes: new sections added. Accepted for publication in Class. Quant. Garv.

References in corpus (22)

• Massive Gravity in Three Dimensions
• Three-Dimensional Gravity Revisited
• More on Massive 3D Gravity
• Topologically Massive Gravity and the AdS/CFT Correspondence
• Note on New Massive Gravity in $Ad{S}_3$
• AdS_3/LCFT_2 - Correlators in New Massive Gravity
• Consistent Boundary Conditions for New Massive Gravity in $Ad{S}_3$
• Generalised Chern-Simons actions for 3d gravity and kappa-Poincare symmetry
• Constraints on extremal self-dual CFTs
• Canonical structure of topologically massive gravity with a cosmological constant
• Asymptotic structure of topologically massive gravity in spacelike stretched AdS sector
• Erratum to `Instability in cosmological topologically massive gravity at the chiral point', arXiv:0805.2610
• Canonical analysis of cosmological topologically massive gravity at the chiral point
• The Evolution of $\Lambda$ Black Holes in the Mini-Superspace Approximation of Loop Quantum Gravity
• Lectures on black holes and the AdS_3 / CFT_2 correspondence
• On Non-handlebody Instantons in 3D Gravity
• AdS_3 Partition Functions Reconstructed
• A Immirzi-like parameter for 3d quantum gravity
• Phase-space and Black Hole Entropy of Higher Genus Horizons in Loop Quantum Gravity
• Symmetries of topological gravity with torsion in the hamiltonian and lagrangian formalisms
• Partition Functions of Three-Dimensional Pure Gravity
• Three-dimensional AdS gravity and extremal CFTs at c=8m

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• A review on geometric formulations for classical field theory: the Bonzom-Livine model for gravity
• Consistent 3D Quantum Gravity on Lens Spaces
• Horizon Mechanics and Asymptotic Symmetries with a Immirzi-like Parameter in 2+1 Dimensions
• Lagrangian generators of the Poincare gauge symmetries
• Effects of curvature and gravity from flat spacetime