On Quantization of Space-time Geometry

Abstract

We consider the outstanding problem of Gravity Quantization. For this reason first we discuss the Geometric Quantization, which begins with defining a mathematical frame work for the algebra of observables that holds equally well for Classical and Quantum Mechanics. We then discuss prequantization, and go into details of the general method of quantization with respect to a polarization using densities and half-forms. This has applications to the theory of unitary group representations and co-adjoint orbits. Also we extend time to a 3-dimensional. And we present a gauge natural formulation of general relativity, and provide some insights into the structure of the space of geometries. Also we show that the quantum gravity effects make the system to evolve from a highly curved semi-classical geometry into a strongly quantum state represented by a weakly curved geometry. Finally we illustrate a prescription for non-perturbatively constructing the Generalized Kodama States, in preparation for subsequent works in this thesis.