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ID: 3201.0, MPI für Gravitationsphysik / Quantum Gravity and Unified Theories
Lorentzian and Euclidean Quantum Gravity - Analytical and Numerical Results
Authors:Ambjörn, Jan; Jurkiewicz, Jerzy; Loll, Renate
Date of Publication (YYYY-MM-DD):2000
Title of Book:M-Theory and Quantum Geometry: Proceedings of the NATO Advanced Study Institute
Start Page:382
End Page:449
Full Name of Book-Editor(s):Larus Thorlacius and Thordur Jonsson
Review Status:not specified
Audience:Not Specified
Abstract / Description:We review some recent attempts to extract information about the nature of quantum gravity, with and without matter, by quantum field theoretical methods. More specifically, we work within a covariant lattice approach where the individual space-time geometries are constructed from fundamental simplicial building blocks, and the path integral over geometries is approximated by summing over a class of piece-wise linear geometries. This method of ''''dynamical triangulations'' is very powerful in 2d, where the regularized theory can be solved explicitly, and gives us more insights into the quantum nature of 2d space-time than continuum methods are presently able to provide. It also allows us to establish an explicit relation between the Lorentzian-and Euclidean-signature quantum theories. Analogous regularized gravitational models can be set up in higher dimensions. Some analytic tools exist to study their state sums, but, unlike in 2d, no complete analytic solutions have yet been constructed. However, a great advantage of our approach is the fact that it is well-suited for numerical simulations. In the second part of this review we describe the relevant Monte Carlo techniques, as well as some of the physical results that have been obtained from the simulations of Euclidean gravity. We also explain why the Lorentzian version of dynamical triangulations is a promising candidate for a non-perturbative theory of quantum gravity
External Publication Status:published
Document Type:InBook
Communicated by:Hermann Nicolai
Affiliations:MPI für Gravitationsphysik/Quantum Gravity and Unified Theories
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