Generalized Lorentzian triangulations and the Calogero Hamiltonian

We introduce and solve a generalized model of (1 + 1)D Lorentzian triangula tions in which a certain subclass of outgrowths is allowed, the occurrence of these being governed by a coupling constant beta. Combining transfer mat rix-, saddle point- and path integral-techniques we show that for beta < 1 it is possible to take a continuum limit in which the model is described by a 1D quantum Calogero Hamiltonian. The coupling constant beta survives the continuum limit and appears as a parameter of the Calogero potential. (C) 2001 Elsevier Science B.V. All rights reserved.