Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2006-09-25
Physics
High Energy Physics
High Energy Physics - Theory
66 pages, 17 figures. Based on the author's thesis for the Master of Science in Theoretical Physics, supervised by R. Loll and
Scientific paper
We describe the motivation behind the recent formulation of a nonperturbative path integral for Lorentzian quantum gravity defined through Causal Dynamical Triangulations (CDT). In the case of two dimensions the model is analytically solvable, leading to a genuine continuum theory of quantum gravity whose ground state describes a two-dimensional "universe" completely governed by quantum fluctuations. One observes that two-dimensional Lorentzian and Euclidean quantum gravity are distinct. In the second part of the review we address the question of how to incorporate a sum over space-time topologies in the gravitational path integral. It is shown that, provided suitable causality restrictions are imposed on the path integral histories, there exists a well-defined nonperturbative gravitational path integral including an explicit sum over topologies in the setting of CDT. A complete analytical solution of the quantum continuum dynamics is obtained uniquely by means of a double scaling limit. We show that in the continuum limit there is a finite density of infinitesimal wormholes. Remarkably, the presence of wormholes leads to a decrease in the effective cosmological constant, reminiscent of the suppression mechanism considered by Coleman and others in the context of a Euclidean path integral formulation of four-dimensional quantum gravity in the continuum. In the last part of the review universality and certain generalizations of the original model are discussed, providing additional evidence that CDT define a genuine continuum theory of two-dimensional Lorentzian quantum gravity.
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