Quantum-mechanical dualities from classical phase space

Abstract

The geometry of the classical phase space C of a finite number of degrees of freedom determines the possible duality symmetries of the corresponding quantum mechanics. Under duality we understand the relativity of the notion of a quantum with respect to an observer on C . We illustrate this property explicitly in the case when classical phase space is complex n-dimensional projective space CP n . We also provide some examples of classical dynamics on CP n that exhibit these properties at the quantum level.