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In mathematical physics, geometric quantization is a mathematical approach to define a quantum theory corresponding to a given classical theory in such a way that certain analogies between the classical theory and the quantum theory remain manifest, for example the similarity between the Heisenberg equation in the Heisenberg picture of quantum mechanics and the Hamilton equation in classical physics.
Symplectic manifolds (describing the phase spaces) play an important role in geometric quantization. One standard method is to construct a Hilbert space based on half-forms.
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