A QUANTUM IS A COMPLEX STRUCTURE ON CLASSICAL PHASE SPACE

JOSÉ M. ISIDRO
2005 International Journal of Geometric Methods in Modern Physics (IJGMMP)  
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
more » ... me 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.
doi:10.1142/s0219887805000673 fatcat:thadhxvmpjgsvg2emtwpyxuzqm