(2+1)-dimensional quantum gravity as the continuum limit of causal dynamical triangulations

D. Benedetti, R. Loll, and F. Zamponi
Phys. Rev. D 76, 104022 – Published 13 November 2007

Abstract

We perform a nonperturbative sum over geometries in a (2+1)-dimensional quantum gravity model given in terms of causal dynamical triangulations. Inspired by the concept of triangulations of product type introduced previously, we impose an additional notion of order on the discrete, causal geometries. This simplifies the combinatorial problem of counting geometries just enough to enable us to calculate the transfer matrix between boundary states labeled by the area of the spatial universe, as well as the corresponding quantum Hamiltonian of the continuum theory. This is the first time in dimension larger than 2 that a Hamiltonian has been derived from such a model by mainly analytical means, and it opens the way for a better understanding of scaling and renormalization issues.

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  • Received 1 June 2007

DOI:https://doi.org/10.1103/PhysRevD.76.104022

©2007 American Physical Society

Authors & Affiliations

D. Benedetti1, R. Loll1, and F. Zamponi2

  • 1Spinoza Institute and Institute for Theoretical Physics, Utrecht University, Leuvenlaan 4, NL-3584 CE Utrecht, The Netherlands
  • 2Service de Physique Théorique, Orme des Merisiers, CEA Saclay, F-91191 Gif-sur-Yvette Cedex, France

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Vol. 76, Iss. 10 — 15 November 2007

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