A Immirzi-like parameter for 3d quantum gravity

Abstract

We study an Immirzi-like ambiguity in three-dimensional quantum gravity. It shares some features with the Immirzi parameter of four-dimensional loop quantum gravity: it does not affect the equations of motion, but modifies the Poisson brackets and the constraint algebra at the canonical level. We focus on the length operator and show how to define it through non-commuting fluxes. We compute its spectrum and show the effect of this Immirzi-like ambiguity. Finally, we extend these considerations to 4d gravity and show how the different topological modifications of the action affect the canonical structure of loop quantum gravity.

14 pages, v2: one reference added, more comments on the 3d/4d comparison

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Cited by in corpus (23)

• The Spin Foam Approach to Quantum Gravity
• $BF$ gravity
• Three-dimensional gravity and Drinfel'd doubles: spacetimes and symmetries from quantum deformations
• Geometric Lagrangian approach to the physical degree of freedom count in field theory
• Testing the role of the Barbero-Immirzi parameter and the choice of connection in Loop Quantum Gravity
• Drinfel'd doubles for (2+1)-gravity
• Towards (3+1) gravity through Drinfel'd doubles with cosmological constant
• Classical r-matrices for the generalised Chern-Simons formulation of 3d gravity
• Faddeev-Jackiw quantization of four dimensional BF theory
• Hamiltonian dynamics of an exotic action for gravity in three dimensions
• 2+1 Quantum Gravity with Barbero-Immirzi like parameter on Toric Spatial Foliation
• Generalizations of the Pontryagin and Husain-Kuchař actions to manifolds with boundary
• Quantization of Lorentzian 3d Gravity by Partial Gauge Fixing
• A review on geometric formulations for classical field theory: the Bonzom-Livine model for gravity
• Horizon Mechanics and Asymptotic Symmetries with a Immirzi-like Parameter in 2+1 Dimensions
• Consistent 3D Quantum Gravity on Lens Spaces
• Canonical and symplectic analysis for three dimensional gravity without dynamics
• Loop Quantization of a Model for D=1+2 (Anti)de Sitter Gravity Coupled to Topological Matter
• Boundary State Stability under Spinfoam Evolution for the Quantum 4-Simplex
• Canonical description of Exotic General Massive Gravity
• Hamilton-Jacobi analysis for three dimensional gravity without dynamics
• Hamiltonian analysis for abelian and non-abelian massive theories in three dimensions
• Complete loop quantization of a dimension 1+2 Lorentzian gravity theory