Related papers: Two-dimensional Quantum Gravity
By restricting the functional integration to the Regge geometries, we give the discretized version of the well known path integral formulation of 2--dimensional quantum gravity in the conformal gauge. We analyze the role played by…
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…
One of several possibilities to construct a quantum theory of gravity is employing the Feynman path integral. This approach is plagued by some problems: the integration measure is not uniquely defined, the Einstein-Hilbert action unbounded,…
The two-dimensional theory of gravity describing a graviton-dilaton system is considered. The graviton-dilaton coupling can be fixed such that the quantum theory remains free of the conformal anomaly for any conformal dimension of the…
Understanding the quantum aspects of gravity is not only a matter of equations and experiments. Gravity is intimately connected with the structure of space and time, and understanding quantum gravity requires us to find a conceptual…
A number of very different approaches to quantum gravity contain a common thread, a hint that spacetime at very short distances becomes effectively two dimensional. I review this evidence, starting with a discussion of the physical meaning…
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…
The goal of this article is to present a broad perspective on quantum gravity for \emph{non-experts}. After a historical introduction, key physical problems of quantum gravity are illustrated. While there are a number of interesting and…
We study the diffusion equation in two-dimensional quantum gravity, and show that the spectral dimension is two despite the fact that the intrinsic Hausdorff dimension of the ensemble of two-dimensional geometries is very different from…
We give a very concise review of the group field theory formalism for non-perturbative quantum gravity, a higher dimensional generalisation of matrix models. We motivate it as a simplicial and local realisation of the idea of 3rd…
Most of the approaches to the construction of a theory of quantum gravity share some principles which do not have specific experimental support up to date. Two of these principles are relevant for our discussion: (i) the gravitational field…
We investigate quantum gravity in four dimensions using the Regge approach on triangulations of the four-torus with general, non-regular incidence matrices. We find that the simplicial lattice tends to develop spikes for vertices with low…
We provide detailed evidence for the claim that nonperturbative quantum gravity, defined through state sums of causal triangulated geometries, possesses a large-scale limit in which the dimension of spacetime is four and the dynamics of the…
Recently an alternate technique for numerical quantum gravity, dynamical triangulation, has been developed. In this method, the geometry is varied by adding and subtracting equilateral simplices from the simplicial complex. This method…
This is an introduction to quantum gravity, aimed at a fairly general audience and concentrating on what have historically two main approaches to quantum gravity: the covariant and canonical programs (string theory is not covered). The…
We describe the idea of studying quantum gravity by means of dynamical triangulations and give examples of its implementation in 2, 3 and 4 space time dimensions. For $d=2$ we consider the generic hermitian 1-matrix model. We introduce the…
A very brief review is given of the current state of research in quantum gravity. Over the past fifteen years, two approaches have emerged as the most promising paths to a quantum theory of gravity: string theory and quantum geometry. I…
The general problems of three-dimensional quantum gravity are recatitulated here, putting the emphasis on the mathematical problems of defining the measure of the path integral over all three-dimensional metrics.This work should be viewed…
Hints from a number of different approaches to quantum gravity point to a phenomenon of "spontaneous dimensional reduction" to two spacetime dimensions near the Planck scale. I examine the physical meaning of the term "dimension" in this…
The two dimensional substructure of general relativity and gravity, and the two dimensional geometry of quantum effect by black hole are disclosed. Then the canonical quantization of the two dimensional theory of gravity is performed. It is…