(2+1)-Dimensional Quantum Gravity as the Continuum Limit of Causal Dynamical Triangulations

Details (2+1)-Dimensional Quantum Gravity as the Continuum Limit of Causal Dynamical Triangulations (2+1)-Dimensional Quantum Gravity as the Continuum Limit of Causal Dynamical Triangulations

2007-04-24

arxiv.org/abs/0704.3214v1

Phys.Rev.D76:104022,2007

Physics

High Energy Physics

High Energy Physics - Theory

38 pages, 13 figures

Scientific paper

10.1103/PhysRevD.76.104022

We perform a non-perturbative 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 labelled 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 two that a Hamiltonian has been derived from such a model by mainly analytical means, and opens the way for a better understanding of scaling and renormalization issues.

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