Generalized Lorentzian triangulations and the Calogero Hamiltonian

We introduce and solve a generalized model of (1+1)D Lorentzian triangulations in which a certain subclass of outgrowths is allowed, the occurrence of these being governed by a coupling constant β. Combining transfer matrix-, saddle point- and path integral-techniques we show that for β<1 it is possible to take a continuum limit in which the model is described by a 1D quantum Calogero Hamiltonian. The coupling constant β survives the continuum limit and appears as a parameter of the Calogero potential.