Editing Canonical quantization (section)

===Classical and quantum brackets===
Dirac's book<ref name="dirac"/> details his popular rule  of  supplanting  [[Poisson bracket]]s   by  [[commutator]]s:
{{Equation box 1
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|equation =   <math>\{A,B\} \longmapsto \tfrac{1}{i \hbar} [\hat{A},\hat{B}] ~.</math>
|cellpadding= 6
|border
|border colour = #0073CF
|background colour=#F9FFF7}}

One might interpret this proposal as saying that we should seek a "quantization map" <math>Q</math> mapping a function <math>f</math> on the classical phase space to an operator <math>Q_f</math> on the quantum Hilbert space such that
<math display="block">Q_{\{f,g\}} = \frac{1}{i\hbar}[Q_f,Q_g]</math>
It is now known that there is no reasonable such quantization map satisfying the above identity exactly for all functions <math>f</math> and {{nowrap|<math>g</math>.}}{{Citation needed|date=April 2023}}