This book explains, in a manner accessible to readers with a knowledge of general relatively and quantum theory acquired from introductory graduate-level courses, the principles of a quantum-geometric unification of these two disciplines. These principles have their roots in the writings of Einstein, Bohr, Born, Dirac, Heisenberg, and other founders of these disciplines. Although their formulation and development has sometimes followed a tortuous path, the origins of this path are clearly visible in those writings, as shown in historical notes provided in appropriate contexts. By taking advantage of recent advances in such areas of modern theoretical physics and mathematics as the fibre bundle theory, gauge fields, group-theoretical methods, coherent states, etc., these principles can be incorporated into quantum geometries that provide the foundations of an extrapolation of general relativity to the quantum regrime. The main goal of this volume is to present the resulting geometry of quantum general relativity in a manner which sets emphasis on fundamental physical ideas and their precise mathematical implementation, and which conforms to the methodologies championed in classical general relativity and in relativistic quantum theory by Einstein and by Dirac, as they founded these respective disciplines. Book jacket.
