Generalized Lorentzian Triangulations and the Calogero Hamiltonian

Abstract

We introduce and solve a generalized model of 1+1D 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 βsurvives the continuum limit and appears as a parameter of the Calogero potential.

47 pages, 5 figures, tex, harvmac, epsf. New title, new introduction, uses a more Stat. Mech. oriented language