The Geometry of Quantum Mechanics

A recent notion in theoretical physics is that not all quantum theories arise from quantising a classical system. Also, a given quantum model may possess more than just one classical limit. These facts find strong evidence in string duality and M–theory, and it has been suggested that they should also have a counterpart in quantum mechanics. In view of these developments we propose dequantisation, a mechanism to render a quantum theory classical. Specifically, we present a geometric procedure to dequantise a given quantum mechanics (regardless of its classical origin, if any) to possibly different classical limits, whose quantisation gives back the original quantum theory. The standard classical limit h̄→ 0 arises as a particular case of our approach.