3d Lorentzian loop quantum gravity and the spinor approach

Understand

We consider the generalization of the "spinor approach" to the Lorentzian case, in the context of 3d loop quantum gravity with cosmological constant $\Lambda=0$.

• The key technical tool that allows this generalization is the recoupling theory between unitary infinite-dimensional representations and non-unitary finite-dimensional ones, obtained in the process of generalizing the Wigner-Eckart theorem to SU(1,1).
• We use SU(1,1) tensor operators to build observables and a solvable quantum Hamiltonian constraint, analogue of the one introduced by V.
• Bonzom and his collaborators in the Euclidean case (with both $\Lambda=0$ and $\Lambda\neq0$).