Related papers: Canonical gravity in two time and two space dimens…

A review is given of some classical and quantum aspects of 2+1 dimensional gravity.

A canonical quantization of two-dimensional gravity minimally coupled to real scalar and spinor Majorana fields is presented. The physical state space of the theory is completely described and calculations are also made of the average value…

Contemporary research programs in fundamental physics appear to suggest that there could be two (physical) times---or none at all. This essay articulates these possibilities in the context of quantum gravity, and in particular of…

Different aspects of relativity, mainly in a canonical formulation, relevant for the question "Is spacetime nothing more than a mathematical space (which describes the evolution in time of the ordinary three-dimensional world) or is it a…

(from the talk:) I shall here speak on gravity in (1+1)-dimensional space-time --- lineal gravity. The purpose of studying lower dimensional theories, and specifically lower dimensional gravity, is to gain insight into difficult…

For a 1+1 dimensional theory of gravity with torsion different approaches to the formulation of a quantum theory are presented. They are shown to lead to the same finite dimensional quantum system. Conceptual questions of quantum gravity…

We use the polygon representation of 2+1--dimensional gravity to explicitly carry out the canonical quantization of a universe with the topology of a torus. The mapping-class-invariant wave function for a quantum ''big bounce'', is…

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…

A classical two dimensional theory of gravity which has a number of interesting features (including a Newtonian limit, black holes and gravitational collapse) is quantized using conformal field theoretic techniques. The critical dimension…

We start a program of background independent quantum gravity in eight dimensions. We begin by considering canonical gravity \textit{a la} "Kaluza-Klein" in $D=d+1$ dimensions. We show that our canonical gravity approach can be applied to…

These lectures briefly review our current understanding of classical and quantum gravity in three spacetime dimensions, concentrating on the quantum mechanics of closed universes and the (2+1)-dimensional black hole. Three formulations of…

General relativity in three spacetime dimensions is used to explore three approaches to the ``problem of time'' in quantum gravity: the internal Schr\"odinger approach with mean extrinsic curvature as a time variable, the Wheeler-DeWitt…

In three spacetime dimensions, general relativity drastically simplifies, becoming a ``topological'' theory with no propagating local degrees of freedom. Nevertheless, many of the difficult conceptual problems of quantizing gravity are…

A formalism previously introduced by the author using tesselated Cauchy surfaces is applied to define a quantized version of gravitating point particles in 2+1 dimensions. We observe that this is the first model whose quantum version…

This is a review of the aspirations and disappointments of the canonical quantization of geometry. I compare the two chief ways of looking at canonical gravity, geometrodynamics and connection dynamics. I capture as much of the classical…

General relativity becomes vastly simpler in three spacetime dimensions: all vacuum solutions have constant curvature, and the moduli space of solutions can be almost completely characterized. As a result, this lower dimensional setting…

Loop Quantum Gravity is widely developed using canonical quantization in an effort to find the correct quantization for gravity. Affine quantization, which is like canonical quantization augmented bounded in one orientation, e.g., a…

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…

Recently 2+1 dimensional gravity theory, especially ${\rm AdS_3}$ has been studied extensively. It was shown to be equivalent to the 2+1 Chern-Simon theory and has been investigated to understand the black hole thermodynamics, i.e. Hawking…

In a recent work we presented a reformulation of the canonical quantum gravity, based on adding the so-called kinematical term to the gravity-matter action; this revised approach leads to a self-consistent canonical quantization of the…