Lorentzian spinfoam propagator

The two-point correlation function is calculated in the Lorentzian Engle-Pereira-Rovelli-Livine spinfoam model and shown to match with the one in Regge calculus in a proper limit: large boundary spins $j\to \infty$ and small Barbero-Immirzi parameter $\gamma \to 0$, keeping the size of the quantum geometry $A\sim \gamma j$ finite and fixed. Compared to the Euclidean case, the definition of a Lorentzian boundary state involves a new feature: the notion of past- and future-pointing intertwiners. The semiclassical correlation function is obtained for a time-oriented semiclassical boundary state.