Turaev-Viro amplitudes from 2+1 Loop Quantum Gravity

Abstract

The Turaev-Viro state sum model provides a covariant spin foam quantization of three-dimensional Riemannian gravity with a positive cosmological constant Λ. We complete the program to canonically quantize the theory in the BF formulation using the formalism of Loop Quantum Gravity. In particular, we show first how quantum group structures arise from the requirement of the constraint algebra to be anomaly free. This allows us to generalize the construction of the physical scalar product, from the Λ = 0 case, in presence of a positive Λ. We prove the equivalence between the covariant and canonical quantizations by recovering the spin foam amplitudes.

23 pages, many figures; v3: minor modifications to match published version

References in corpus (4)

• Observables in Loop Quantum Gravity with a cosmological constant
• Chern-Simons theory, Stokes' Theorem, and the Duflo map
• Deformed phase space for 3d loop gravity and hyperbolic discrete geometries
• Modelling black holes with angular momentum in loop quantum gravity

Cited by in corpus (29)

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• Towards the Turaev-Viro amplitudes from a Hamiltonian constraint
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• Origin of the quantum group symmetry in 3d quantum gravity
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• $q$-deformed 3D Loop Gravity on the Torus
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• Extensions of the Duflo map and Chern-Simons expectation values
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