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properties 1 & 2, along with a weaker condition that 3 be true only asymptotically in the limit (see Moyal bracket), leads to deformation quantization, and some extraneous information must be provided, as in the standard theories utilized in most of physics. Accepting properties 1 & 2 & 3 but restricting the space of quantizable observables to exclude terms such as the cubic ones in the above example amounts to geometric quantization.

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