| Geometric Quantization |
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| CATEGORIES ABOUT GEOMETRIC QUANTIZATION | |
| symplectic geometry | |
| mathematical quantization | |
| functional analysis | |
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One of the earliest attempts at a natural quantization was Weyl Quantization , done by Hermann Weyl in 1927 . Here, an attempt is made to associate a quantum-mechanical observable (a Self-adjoint Operator on a Hilbert Space ) with a real-valued function on classical Phase Space . Here, the position and momentum are reinterpreted as the generators of the Heisenberg Group , and the Hilbert space appears as a Group Representation of the Heisenberg group. In 1949 , Moyal considered the product of a pair of such observables and asked what the corresponding function would be on the classical phase space. This lead him to define the Moyal Product of a pair of functions. More generally, this technique leads to Deformation Quantization , where the Moyal product is taken to be a deformation of the algebra of functions on a Symplectic Manifold or Poisson Manifold . SEE ALSO EXTERNAL LINKS
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