Related papers: On the validity of ADM formulation in 2D quantum g…
We have examined a modified dilaton gravity whose action is separable into the kinetic and the cosmological terms for the sake of the quantization. The black hole solutions survive even in the quantized theory, but the ADM mass of the…
A two-loop (cylinder) amplitude of the 2d pure gravity theory is obtained in the proper-time gauge ($g_{00}=1$, $g_{01}=g_{10}=0$) in the continuum formulation. The constraint $T_{01}=0$ is solved and used to reduce the problem of field…
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…
Quantum gravity is investigated in the limit of a large number of space-time dimensions, using as an ultraviolet regularization the simplicial lattice path integral formulation. In the weak field limit the appropriate expansion parameter is…
We propose a new type of gauge in two-dimensional quantum gravity. We investigate pure gravity in this gauge, and find that the system reduces to quantum mechanics of loop length $l$. Furthermore, we rederive the $c\!=\!0$ string field…
We study a new two-dimensional quantum gravity theory, based on a gravitational action containing both the familiar Liouville term and the Mabuchi functional, which has been shown to be related to the coupling of non-conformal matter to…
Loop Quantum Gravity heavily relies on a connection formulation of General Relativity such that 1. the connection Poisson commutes with itself and 2. the corresponding gauge group is compact. This can be achieved starting from the Palatini…
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…
Loop quantum gravity and cosmology are reviewed with an emphasis on evaluating the dynamics, rather than constructing it. The three crucial parts of such an analysis are (i) deriving effective equations, (ii) controlling the theory's…
We use the mathematical framework of loop quantum gravity (LQG) to study the quantization of three dimensional (Riemannian) gravity with positive cosmological constant (Lambda>0). We show that the usual regularization techniques (successful…
The constraint structure of 2D-gravity with the Weyl and area-preserving diffeomorphism invariances is analysed in the ADM formulation. It is found that when the area-preserving diffeomorphism constraints are kept, the usual conformal gauge…
In this paper, an attempt is made to represent 5+1 dimensional gravity (via ADM formalism) in terms of the loop constructions introduced by the author in a companion paper. The "momenta" and "velocity" from the earlier paper, which were…
2D $R^2$ quantum gravity in infinitely large invariant volume is considered. In weak coupling limit the dynamics is reduced to quantum mechanics of a single degree of freedom. The correspondent two - point Green function is calculated…
We do not yet know how to quantize gravity in 3+1 dimensions, but in lower dimensions we face the opposite problem: many of the approaches originally developed for (3+1)-dimensional gravity can be successfully implemented in 2+1 dimensions,…
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…
The formula existing in the literature for the ADM mass of 2D dilaton gravity is incomplete. For example, in the case of an infalling matter shockwave this formula fails to give a time-independent mass, unless a very special coordinate…
The continuum (Liouville) approach to the two-dimensional (2-D) quantum gravity is reviewed with particular attention to the $c=1$ conformal matter coupling, and new results on a related problem of dilaton gravity are reported. After…
We formulate quantum gravity in $2+\epsilon$ dimensions in such a way that the conformal mode is explicitly separated. The dynamics of the conformal mode is understood in terms of the oversubtraction due to the one loop counter term. The…
We consider two-dimensional quantum gravity coupled to matter fields which are renormalizable, but not conformal invariant. Questions concerning the $\b$ function and the effective action are addressed, and the effective action and the…
After reviewing the basic aspects of the exactly solvable quantum-corrected dilaton-gravity theories in two dimensions, we discuss a (subjective) selection of other aspects: a) supersymmetric extensions, b) canonical formalism, ADM-mass,…