Non-Standard Phase Space Variables, Quantization and Path-Integrals, or Little Ado about Much

Summary

INTRODUCTION

In this article we want to describe a long-term research project that the authors plan to carry out over a period in the immediate future. We would like to outline the basic ideas of the project and give a few preliminary calculations the bear on the validity of our ideas as well as some speculations on where the research will lead. We chose this volume to do this because it occured to us that each of the components of our plan lies in a field that Charlie has touched on at some point in his varied career. These components are the Hamiltonian formulation of the gravitational field equations, path integral quantization, and quantum cosmology. Such a wide-ranging list shows how much we all owe to Charlie as a scientist and we hope that our efforts will demonstrate our debt to his lead in these fields.

The genesis of our paper lies in a long-term concern that both of us have had about the structure of quantum mechanics that has been the subject of years of blackboard discussions between us (the speculations of one of us [M.R.] go all the way back to fondly-remembered discussions with Charlie and other Charlie-students in Maryland). The focal point of our ideas has always been the cookbook nature of quantum mechanics as based on a Hamiltonian action functional for the classical equations of motion and canonical commutation relations derived from the Poisson bracket relations of the variables in the action.