Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2004-07-19
Int.J.Geom.Meth.Mod.Phys. 2 (2005) 633-655
Physics
High Energy Physics
High Energy Physics - Theory
Scientific paper
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.
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