Hexagon model for 3D Lorentzian quantum cosmology

B. Dittrich and R. Loll
Phys. Rev. D 66, 084016 – Published 29 October 2002
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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.

  • Received 12 July 2002

DOI:https://doi.org/10.1103/PhysRevD.66.084016

©2002 American Physical Society

Authors & Affiliations

B. Dittrich

  • Max-Planck-Institute for Gravitational Physics, Am Mühlenberg 1, D-14476 Golm, Germany

R. Loll

  • Institute for Theoretical Physics, Utrecht University, Leuvenlaan 4, NL-3584 CE Utrecht, The Netherlands

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Issue

Vol. 66, Iss. 8 — 15 October 2002

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