  Duality transformations within the quantum mechanics of a finite number of
degrees of freedom can be regarded as the dependence of the notion of a
quantum, i.e., an elementary excitation of the vacuum, on the observer on
classical phase space. Under an observer we understand, as in general
relativity, a local coordinate chart. While classical mechanics can be
formulated using a symplectic structure on classical phase space, quantum
mechanics requires a complex-differentiable structure on that same space.
Complex-differentiable structures on a given real manifold are often not
unique. This article is devoted to analysing the dependence of the notion of a
quantum on the complex-differentiable structure chosen on classical phase
space.
