Turaev-Viro amplitudes from 2+1 Loop Quantum Gravity

Understand

The Turaev-Viro state sum model provides a covariant spin foam quantization of three-dimensional Riemannian gravity with a positive cosmological constant {\Lambda}.

• 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 {\Lambda} = 0 case, in presence of a positive {\Lambda}.