LQG vertex with finite Immirzi parameter

Understand

We extend the definition of the "flipped" loop-quantum-gravity vertex to the case of a finite Immirzi parameter.

• We cover the Euclidean as well as the Lorentzian case.
• We show that the resulting dynamics is defined on a Hilbert space isomorphic to the one of loop quantum gravity, and that the area operator has the same discrete spectrum as in loop quantum gravity.
• This includes the correct dependence on the Immirzi parameter, and, remarkably, holds in the Lorentzian case as well.