D2 - New Hamiltonian variables

Summary

The present status of the new variables program for canonical quantum gravity is discussed. A summary is given of the papers which were presented at the New Variables Workshop at GR-12, and particular attention is given to those issues which are crucial at the present stage of development of this program. Chief among these issues is whether a theory can be quantized nonperturbatively in the absence of any information about the physical observables algebra of the corresponding classical theory. Finally, a wild speculation about the relationship between nonperturbative quantum general relativity and perturbative string theory is made.

Introduction

Abhay Ashtekar introduced his new variables in the Fall of 1985. In the intervening four years this new formalism has been developed and applied to both classical and quantum general relativity. On both sides significant new results have been achieved, and these developments are being actively pursued by a growing number of people. It was thus appropriate to have a workshop at GR-12 dedicated to this subject. In this, a summary of that workshop, I will try to describe briefly several of the directions that this work has taken, with an emphasis on the present status and open problems. In doing so I will touch on each of the six presentations that were given in the workshop, but I will not strictly follow the format of the workshop itself.