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by commutators:

One might interpret this proposal as saying that we should seek a "quantization map" mapping a function on the classical phase space to an operator on the quantum Hilbert space such that

It is now known that there is no reasonable such quantization map satisfying the above identity exactly for all functions and $g$.

Groenewold's theorem

One concrete version of the above impossibility claim is Groenewold's theorem (after Dutch theoretical physicist

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