Recent Mathematical Developments in Quantum General Relativity

Abstract

After a brief chronological sketch of developments in non-perturbative canonical quantum gravity, some of the recent mathematical results are reviewed. These include: i) an explicit construction of the quantum counterpart of Wheeler's superspace; ii) a rigorous procedure leading to the general solution of the diffeomorphism constraint in quantum geometrodynamics as well as connection dynamics; and, iii) a scheme to incorporate the reality conditions in quantum connection dynamics. Furthermore, there is a new language to formulate the central questions and techniques to answer them. These developments put the program on a sounder footing and, in particular, address certain concerns and reservations about consistency of the overall scheme.

14 pages, TEX, no figures, Preprint CGPG-94/9-4

Cited by in corpus (11)

• Projective Techniques and Functional Integration
• Differential Geometry on the Space of Connections via Graphs and Projective Limits
• Spin Network States in Gauge Theory
• NON-PERTURBATIVE SOLUTIONS FOR LATTICE QUANTUM GRAVITY
• Knots and Quantum Gravity: Progress and Prospects
• The space of states of quantum gravity in terms of loops and extended loops: some remarks
• Bibliography of publications related to Classical and Quantum Gravity in terms of Connection and Loop Variables
• Generalization Of Lorentz-Poincare Ether Theory To Quantum Gravity
• Coherent State Transforms for Spaces of Connections
• Does matter differ from vacuum?
• Postrelativity --- A Paradigm For Quantization With Preferred Newtonian Frame