Geometric Quantization
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
.
See also
Heisenberg group
External links
William Ritter's review of Geometric Quantization
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