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.

(2+1)-dimensional quantum gravity as the continuum limit of causal dynamical triangulations / Benedetti, D; Loll, R; Zamponi, F. - In: PHYSICAL REVIEW D, PARTICLES, FIELDS, GRAVITATION, AND COSMOLOGY. - ISSN 1550-7998. - 76:10(2007). [10.1103/PhysRevD.76.104022]

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

Zamponi F
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.
2007
Quantum gravity; triangulations; random geometry
01 Pubblicazione su rivista::01a Articolo in rivista
(2+1)-dimensional quantum gravity as the continuum limit of causal dynamical triangulations / Benedetti, D; Loll, R; Zamponi, F. - In: PHYSICAL REVIEW D, PARTICLES, FIELDS, GRAVITATION, AND COSMOLOGY. - ISSN 1550-7998. - 76:10(2007). [10.1103/PhysRevD.76.104022]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1693827
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