The structure of phase space and quantum mechanics

Abstract

The author and his collaborators I-6) have been interested for a number of years in the structure of phase space as a carrier of canonical transformations, and in the representations of the latter in quantum mechanics. This has led to their conviction that some quantum features, such as the nature of the spectra of Hamiltonians i.e.,continuous, discrete, mixed or of bands, are already implicit in the classical picture. The main new development in this field was the recent discussion of the canonical transformation to action and angle variables for periodic potentials and their representation in quantum mechanics. 4) In this note though, we shall try to give a general overview of our program and indicate the references where the reader can find a more systematic analysis.