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 the presence of a positive Λ. We prove the equivalence between the covariant and canonical quantizations by recovering the spin foam amplitudes. © 2014 American Physical Society.

Turaev-Viro amplitudes from 2+1 Loop Quantum Gravity / Pranzetti, Daniele. - In: PHYSICAL REVIEW D, PARTICLES, FIELDS, GRAVITATION, AND COSMOLOGY. - ISSN 1550-7998. - 89:8(2014), pp. 1-14. [10.1103/PhysRevD.89.084058]

Turaev-Viro amplitudes from 2+1 Loop Quantum Gravity

Pranzetti, Daniele
2014-01-01

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 the presence of a positive Λ. We prove the equivalence between the covariant and canonical quantizations by recovering the spin foam amplitudes. © 2014 American Physical Society.
2014
89
8
1
14
084058
http://inspirehep.net/record/1280913
https://arxiv.org/abs/1402.2384
Pranzetti, Daniele
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/32556
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