  On classical phase spaces admitting just one complex-differentiable
structure, there is no indeterminacy in the choice of the creation operators
that create quanta out of a given vacuum. In these cases the notion of a
quantum is universal, i.e., independent of the observer on classical phase
space. Such is the case in all standard applications of quantum mechanics.
However, recent developments suggest that the notion of a quantum may not be
universal. Transformations between observers that do not agree on the notion of
an elementary quantum are called dualities. Classical phase spaces admitting
more than one complex-differentiable structure thus provide a natural framework
to study dualities in quantum mechanics. As an example we quantise a classical
mechanics whose phase space is a torus and prove explicitly that it exhibits
dualities.
