DMCA
A hexagon model for 3D Lorentzian quantum cosmology (2002)
| Venue: | PHYS. REV. D |
| Citations: | 18 - 6 self |
BibTeX
@ARTICLE{Dittrich02ahexagon,
author = {B. Dittrich and R. Loll},
title = {A hexagon model for 3D Lorentzian quantum cosmology},
journal = {PHYS. REV. D},
year = {2002},
pages = {307263}
}
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Abstract
We formulate a dynamically triangulated model of three-dimensional Lorentzian quantum gravity whose spatial sections are flat two-tori. It is shown that the combinatorics involved in evaluating the one-step propagator (the transfer matrix) is that of a set of vicious walkers on a two-dimensional lattice with periodic boundary conditions and that the entropy of the model scales exponentially with the volume. We also give explicit expressions for the Teichmüller parameters of the spatial slices in terms of the discrete parameters of the 3d triangulations, and reexpress the discretized action in terms of them. The relative simplicity and explicitness of this model make it ideally suited for an analytic study of the conformal-factor cancellation observed previously in Lorentzian dynamical triangulations and of its relation to alternative, reduced phase space quantizations of 3d gravity.
Keyphrases
lorentzian quantum cosmology hexagon model analytic study explicit expression periodic boundary condition transfer matrix one-step propagator discretized action conformal-factor cancellation lorentzian dynamical triangulation spatial section triangulated model phase space quantization discrete parameter three-dimensional lorentzian quantum gravity two-dimensional lattice spatial slice relative simplicity vicious walker teichm ller parameter
