On the geometry of geometric quantization
Ennio Gozzi, University of Trieste
In this talk we will pedagogically review the Hilbert space approach to Classical Mechanics pioneered by Koopman and von Neumann. Next we will build its associated Classical Path Integral and study geometrically the many extra variables which make their appearance beside the phase-space ones. Quantization turns then out to be nothing else than a proper dimensional reduction and to be at the same time the functional counterpart of Geometric Quantization.