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Recent Mathematical Developments in Quantum General Relativity
Abhay Ashtekar
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 explici…
A Manifestly Gauge-Invariant Approach to Quantum Theories of Gauge Fields
A. Ashtekar, J. Lewandowski, D. Marolf +2
In gauge theories, physical histories are represented by space-time connections modulo gauge transformations. The space of histories is thus intrinsically non-linear. The standard…
A Striking Property of the Gravitational Hamiltonian
Abhay Ashtekar, Madhavan Varadarajan
{\sl A Hamiltonian framework for 2+1 dimensional gravity coupled with matter (satisfying positive energy conditions) is considered in the asymptotically flat context. It is shown t…
An algebraic extension of Dirac quantization: Examples
A. Ashtekar, Ranjeet S. Tate
An extension of the Dirac procedure for the quantization of constrained systems is necessary to address certain issues that are left open in Dirac's original proposal. These issues…
New Loop Representations for 2+1 Gravity
A. Ashtekar, R. Loll
Since the gauge group underlying 2+1-dimensional general relativity is non-compact, certain difficulties arise in the passage from the connection to the loop representations. It is…
Quantum Gravity: A Mathematical Physics Perspective
Abhay Ashtekar
This article is based on an invited talk given at the Workshop on Mathematical Physics Towards XXIst Century, held at Beer-Sheva, Israel in 1993. It contains an introduction to qua…
Integration on the space of Connections Modulo Gauge Transformations
Abhay Ashtekar, Donald Marolf, Jose Mourao
A summary of the known results on integration theory on the space of connections modulo gauge transformations is presented and its significance to quantum theories of gauge fields…
Overview and Outlook
Abhay Ashtekar
This report is based on the talk given by the author in the concluding session of the workshop on Canonical Methods in Classical and Quantum General Relativity, held a Bad-Honef, G…