Related papers: Two-dimensional Quantum Gravity
An assessment is offered of the progress that the major approaches to quantum gravity have made towards the goal of constructing a complete and satisfactory theory. The emphasis is on loop quantum gravity and string theory, although other…
In the last 20 years, loop quantum gravity, a background independent approach to unify general relativity and quantum mechanics, has been widely investigated. The aim of loop quantum gravity is to construct a mathematically rigorous,…
Starting from the work of the author in 1990 with different collaborators, essential progress in 2d gravity theories has been made. Now all such theories (and not only certain special models) can be treated at the classical as well as at…
The aim of this dissertation is to review `Loop Quantum Gravity', explaining the main structure of the theory and indicating its main open issues. We will develop the two main lines of research for the theory: the canonical quantization…
We study a c=-2 conformal field theory coupled to two-dimensional quantum gravity by means of dynamical triangulations. We define the geodesic distance r on the triangulated surface with N triangles, and show that dim[r^{d_H}]= dim[N],…
We provide a non-perturbative geometrical characterization of the partition function of $n$-dimensional quantum gravity based on a coarse classification of riemannian geometries. We show that, under natural geometrical constraints, the…
A viable quantum theory of gravity is one of the biggest challenges facing physicists. We discuss the confluence of two highly expected features which might be instrumental in the quest of a finite and renormalizable quantum gravity --…
No theory of four-dimensional quantum gravity exists as yet. In this situation the two-dimensional theory, which can be analyzed by conventional field-theoretical methods, can serve as a toy model for studying some aspects of quantum…
The quest for a consistent theory which describes the quantum microstructure of spacetime seems to require some departure from the paradigms that have been followed in the construction of quantum theories for the other fundamental…
The problem of constructing a quantum theory of gravity is considered from a novel viewpoint. It is argued that any consistent theory of gravity should incorporate a relational character between the matter constituents of the theory. In…
Causal dynamical triangulations (CDT) can be used as a regularization of quantum gravity. In two dimensions the theory can be solved anlytically, even before the cut-off is removed and one can study in detail how to take the continuum…
The quantum group structure of the Liouville theory is reviewd and shown to be an important tool for solving the theory.
In this paper we have calculated the spectral dimension of loop quantum gravity (LQG) using simple arguments coming from the area spectrum at different length scales. We have obtained that the spectral dimension of the spatial section runs…
We develop a transfer matrix formalism for two-dimensional pure gravity. By taking the continuum limit, we obtain a "Hamiltonian formalism'' in which the geodesic distance plays the role of time. Applying this formalism, we obtain a…
We present a new model of quantum gravity as a theory of random geometries given explicitly in terms of a multitrace matrix model. This is a generalization of the usual discretized random surfaces of 2D quantum gravity which works away from…
Exactly soluble models can serve as excellent tools to explore conceptual issues in non-perturbative quantum gravity. In perturbative approaches, it is only the two radiative modes of the linearized gravitational field that are quantized.…
We show that there exists a divergent correlation length in 2d quantum gravity for the matter fields close to the critical point provided one uses the invariant geodesic distance as the measure of distance. The corresponding…
Topological gravity is equivalent to physical gravity in two dimensions in a way that is still mysterious, though by now it has been proved by Kontsevich. In this paper it is shown that a similar relation between topological and physical…
In this review, the fundamental structure of loop quantum gravity is presented pedagogically. Our main aim is to help non-experts to understand the motivations, basic structures, as well as general results. It may also be beneficial to…
In the investigation and resolution of the cosmological constant problem the inclusion of the dynamics of quantum gravity can be a crucial step. In this work we suggest that the quantum constraints in a canonical theory of gravity can…