SOME CONSEQUENCES OF PHASE SPACE QUANTUM GEOMETRY

Julian Schwinger

G. Papini

Ricardo Alejandro Troncoso Perez, Cristian Andres Martinez Silva

Basil J. Hiley

Hoshang Heydari

John R. Klauder

Phase space is the state space of classical mechanics, and this manifold is normally endowed only with a symplectic form. The geometry of quantum mechanics is necessarily more complicated. Arguments will be given to show that augmenting the symplectic manifold of classical phase space with a Riemannian metric is sufficient for describing quantum mechanics. In particular, using such spaces, a fully satisfactory geometric version of quantization will be developed and described.