Sabir, Abdenour

Perhaps constructing a complete theory of quantum gravity, has been one of the greatest challenges for theoretical physicists in the last few decades, a theory that would reconcile general relativity and quantum mechanics. Addressing this issue, we are drawing a parallel between the Schrodinger and Klein-Gordon equation in quantum mechanics and Schrodinger-based or Klein-Gordon based wave equation in canonical quantum gravity. In particular we analyze the quantum geometrodynamics Schrodinger equation for a homogeneous cosmological model and we study the quantum field effects for the &PHgr;6 scalar field in Kantowski-Sachs universe. In essence, we present a unified view of quantum gravity by establishing a parallel between our study and the usual quantum mechanics. Thus, the first part of this dissertation deals with the quantization of Bianchi type IX space-time where the concept of time is derived by imposing the constraints as expectation values over the true dynamical-degrees of freedom of the gravitational field. Thus, we obtained a Schrodinger type wave equation instead of the Wheeler-DeWitt which is associated with the problem of time in quantum gravity [1]. The main technical difference between our proposed equation and other quantum cosmology approaches is in our treatment of the constraints. Ordinarily, the equation cannot be solved simply by separating the coordinates variables, and only under some specific conditions imposed on the background that one may obtain exact analytical expressions. In the second part, we evaluated the one-loop renormalized effective potential for the massive self interacting &PHgr;6 theory the spatially homogenous and anisotropic Kantowki-Sachs Universe. We concluded that regularizing the theory in (3 + 1) dimensional space-time may not be possible. Finally, we looked at the time evolution of the critical temperature that is associated with our model.