Spherically symmetric models in loop quantum gravity

Abstract

Loop quantum gravity (LQG) is one of the most promising enterprises towards a quantum theory of gravity. The search for a theory of quantum gravity is motivated by the belief that such a framework may solve most of the inconsistencies of the two today's accepted and prominent models of nature - general relativity (GR) and the standard model of particle physics, which is described by quantized field theories.<br />The development of symmetry reduced models is of great importance, since these models render calculations more manageable than in the full theory. The theory of gravitation ows its success to such models since Newton, in particular the spherically symmetric ones, which are designed to describe the gravitational field of astrophysical objects, such as planets, stars of all kinds, and blackholes. If the angular momentum of such objects is sufficiently small calculations fit extremely well to observational data. Another example for the success of symmetry reduced models is, of course, the FRW model in cosmology.<br />This thesis aims at working out the classical part of symmetry reduction used in LQG in general and at presenting a spherically symmetric model and its quantization inspired by LQG. Thereby it retraces the construction of full LQG. Furthermore, it presents the loop quantized version of gravity coupled to Yang-Mills fields in general and spherically symmetric LQG coupled to spherically symmetric (loop quantum) electrodynamics in particular.