Sommaire:

I will show how the usual Loop Quantum Gravity phase space can be deformed to characterize hyperbolic discrete geometries and thus be a candidate to describe the discretization of SU(2) BF theory with a (negative) cosmological constant. The quantization of this model will then give at the kinematical level, an Hilbert space spanned by spin networks built on Uq(su(2)) (with q real). I will also build an Hamiltonian constraint and show that the Turaev-Viro amplitude with q real is a solution of the quantum Hamiltonian. This model is therefore a natural candidate to describe 3D loop quantum gravity with a (negative) cosmological constant.

Pour plus d'informations, merci de contacter Alexandrov S.