Related papers: Exact Operator Quantization of a Model of Two-Dime…
A model for 2D Quantum Gravity is constructed out of the Virasoro group. To this end the quantization of the abstract Virasoro group is revisited. For the critical values of the conformal anomaly c, some quantum operators (SL(2,R)…
In this article we introduce a new operator representing the three-dimensional scalar curvature in loop quantum gravity. Our construction does not apply to the entire kinematical Hilbert space of loop quantum gravity; instead, the operator…
We show how it is possible to formulate Euclidean two-dimensional quantum gravity as the scaling limit of an ordinary statistical system by means of dynamical triangulations, which can be viewed as a discretization in the space of…
We consider the background-free quantum gravity based on conformal gravity with the Riegert-Wess-Zumino action, which is formulated in terms of a conformal field theory. Employing the $R \times S^3$ background in practice, we construct the…
In this habilitation thesis we provide an introduction to gravitational models in two spacetime dimensions. Focus is put on exactly solvable models. We begin by introducing and motivating different possible gravitational actions, including…
Euclidean dilaton gravity in two dimensions is studied exploiting its representation as a complexified first order gravity model. All local classical solutions are obtained. A global discussion reveals that for a given model only a…
We show that the quantization of spherically symmetric pure gravity can be carried out completely in the framework of Ashtekar's self-dual representation. Consistent operator orderings can be given for the constraint functionals yielding…
We study the quantum properties of an oscillator in proper time. This proper time oscillator is a particle model with mass that is on shell. Its internal time can be treated as a self-adjoint operator. The displaced time and displaced time…
We study a two-dimensional conformal field theory coupled to quantum gravity on a disk. Using the continuum Liouville field approach, we compute three-point correlation functions of boundary operators. The structure of momentum…
We discuss the renormalization of Einstein-Hilbert's gravity in $d=2+\epsilon$ dimensions. We show that the application of the path-integral approach leads naturally to scheme- and gauge-independent results on-shell, but also gives a…
We present a covariant quantization scheme for the so-called "partially massless" graviton field in de Sitter spacetime. Our approach is founded on the principles of the de Sitter group representation theory (in the sense given by Wigner),…
We present a review of the canonical quantization approach to the problem of non-perturbative 2d dilaton gravity. In the case of chiral matter we describe a method for solving the constraints by constructing a Kac-Moody current algebra. For…
In order to test the canonical quantization programme for general relativity we introduce a reduced model for a real sector of complexified Ashtekar gravity which captures important properties of the full theory. While it does not…
On the basis of dynamic quantization method we build in this paper a new mathematically correct quantization scheme of gravity. In the frame of this scheme we develop a canonical formalism in tetrad-connection variables in 4-D theory of…
We present a detailed account of the isomonodromic quantization of dimensionally reduced Einstein gravity with two commuting Killing vectors. This theory constitutes an integrable ``midi-superspace" version of quantum gravity with…
This work demonstrates that a complete description of the interaction of matter and all forces, gravitational and non-gravitational, can in fact be realized within a quantum affine algebraic framework. Using the affine group formalism, we…
The nature of the classical canonical phase-space variables for gravity suggests that the associated quantum field operators should obey affine commutation relations rather than canonical commutation relations. Prior to the introduction of…
After carefully regularizing the Wheeler -- De Witt operator, which is the Hamiltonian operator of canonical quantum gravity, we find a class of exact solutions of the Wheeler -- De Witt equation.
We formulate a non-perturbative lattice model of two-dimensional Lorentzian quantum gravity by performing the path integral over geometries with a causal structure. The model can be solved exactly at the discretized level. Its continuum…
The quantization of the gravitational field is discussed within the exact uncertainty approach. The method may be described as a Hamilton-Jacobi quantization of gravity. It differs from previous approaches that take the classical…