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Recent Mathematical Developments in Quantum General Relativity

Abhay Ashtekar
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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.

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Abhay Ashtekar. 1994-11-23. Recent Mathematical Developments in Quantum General Relativity. https://arxiv.org/abs/gr-qc/9411055

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