  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 $\Lambda\neq0$). We show that the Lorentzian Ponzano-Regge
amplitude is solution of the quantum Hamiltonian constraint by recovering the
Biedenharn-Elliott relation (generalized to the case where unitary and
non-unitary SU(1,1) representations are coupled to each other). Our formalism
is sufficiently general that both the Lorentzian and the Euclidean case can be
recovered (with $\Lambda=0$).

General Relativity and Quantum Cosmology;High Energy Physics - Theory