Generalized Lorentzian Triangulations and the Calogero Hamiltonian

TL;DR

This paper introduces a generalized 1+1D Lorentzian triangulation model with outgrowths controlled by a coupling constant, demonstrating that its continuum limit is described by a quantum Calogero Hamiltonian with the coupling parameter preserved.

Contribution

It extends Lorentzian triangulation models by incorporating outgrowths and establishes a connection to the Calogero Hamiltonian in the continuum limit.

Findings

Continuum limit described by 1D quantum Calogero Hamiltonian

Coupling constant  survives in the continuum limit

Model solvable using transfer matrix, saddle point, and path integral techniques

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 \beta. Combining transfer matrix-, 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.