2007/04/24 by D. Benedetti, Dario Benedetti, R. Loll +2 · 3 citations
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Noncommutative and Quantum Gravity Theories #gr-qc #hep-th
paper · pdf · doi:10.1103/physrevd.76.104022
published as Phys.Rev.D76:104022,2007 · 38 pages, 13 figures
arxiv created 2007/04/24 · openalex publication_date 2007/11/13 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
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.