Observables and dynamics in quantum gravity

Abstract

The treatment of quantum constraint theories in physics is considered. These systems exist in many different branches of physics. One noticeable case is the quantum theory of gravity (which is a completely constraint system). We contrast two modern methods of solving such quantum constraint systems, namely the method used in the String Theory - BRST Quantization, and that used in Loop Quantum Gravity - the Loop Quantization. We investigate these methods and the quantum solution space they produce - along with proper observables - for the case of a discrete closed string. This system has the advantage that it lends itself to the investigation of these two methods of quantization easily - thereby highlighting some of their principle features - yet it is simple enough so to side-step the many complications that arise in more general systems.Science, Faculty ofPhysics and Astronomy, Department ofGraduat