Related papers: Canonical gravity in two time and two space dimens…
Several investigations in the study of cosmological structure formation use numerical simulations in both two and three dimensions. In this paper we address the subtle question of ambiguities in the nature of two dimensional gravity in an…
As a preparation for its quantization in the loop formalism, the 2-dimensional gravitation model of Jackiw and Teitelboim is analysed in the classical canonical formalism. The dynamics is of pure constraints as it is well-known. A partial…
For a certain example of a "doubly special relativity theory" the modified space-time Lorentz transformations are obtained from momentum space transformations by using canonical methods. In the sequel an energy-momentum dependent space-time…
Using a PASCAL program to follow the evolution of two gravitating particles in 2+1 dimensions we find solutions in which the particles wind around one another indefinitely. As their center of mass moves `tachyonic' they form a Gott-pair. To…
A canonical quantization for two dimensional gravity models, including a dilaton gravity model, is performed in a way suitable for the light-cone gauge. We extend the theory developed by Abdalla {\it et.al.}\cite{AM} and obtain the…
We review a recently discovered continuum limit for the one-matrix model which describes "causal" two-dimensional quantum gravity. The behaviour of the quantum geometry in this limit is different from the quantum geometry of Euclidean…
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…
I discuss recent progress in our understanding of two barriers in quantum gravity: $c > 1$ in the case of 2d quantum gravity and $D > 2$ in the case of Euclidean Einstein-Hilbert gravity formulated in space-time dimensions $D >2$.
Non-abelian higher gauge theory has recently emerged as a generalization of standard gauge theory to higher dimensional (2-dimensional in the present context) connection forms, and as such, it has been successfully applied to the…
We present an introduction to the canonical quantization of gravity performed in loop quantum gravity, based on lectures held at the 3rd quantum geometry and quantum gravity school in Zakopane in 2011. A special feature of this introduction…
Extra dimensions can be utilized to simplify problems in classical mechanics, offering new insights. Here we show a simple example of how the motion of a test particle under the influence of an inverse-quadratic potential in 1D is…
We provide compelling evidence that a previously introduced model of non-perturbative 2d Lorentzian quantum gravity exhibits (two-dimensional) flat-space behaviour when coupled to Ising spins. The evidence comes from both a high-temperature…
Two-dimensional quantum gravity with an $R^2$ term is investigated in the continuum framework. It is shown that the partition function for small area $A$ is highly suppressed by an exponential factor $exp \{ -2\pi (1-h)^2/(m^2A) \}$, where…
In prior work, we have argued that spacetime functionalism provides tools for clarifying the conceptual difficulties specifically linked to the emergence of spacetime in certain approaches to quantum gravity. We argue in this article that…
We survey some philosophical aspects of the search for a quantum theory of gravity, emphasising how quantum gravity throws into doubt the treatment of spacetime common to the two `ingredient theories' (quantum theory and general…
I investigate the relationship between the phase space path integral in (2+1)-dimensional gravity and the canonical quantization of the corresponding reduced phase space in the York time slicing. I demonstrate the equivalence of these two…
We give an explicitly gauge invariant canonical analysis of linearized quadratic gravity theories in three dimensions for both flat and de-Sitter backgrounds. In flat backgrounds, we also study the effects of gravitational Chern-Simons…
A 4-dimensional Lorentzian static space-time is equivalent to 3-dimensional Euclidean gravity coupled to a massless Klein-field. By canonically quantizing the coupling model in the framework of loop quantum gravity, we obtain a quantum…
This essay presents an accessible introduction to the basic motivations to seek a quantum theory of gravity. It focuses on one approach- loop quantum gravity - as an example of the rich philosophical issues that arise when we try to combine…
An important task faced by all approaches of quantum gravity is to incorporate superpositions and quantify quantum uncertainties of spacetime causal relations. We address this task in 2D. By identifying a global $Z_2$ symmetry of 1+1D…