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In QFT, we transform a classical lagrangian into a quantum one by transforming our scalar fields into quantum operators. To do so we chose an ordering (Weyl or normal ordering for example), and we impose commutations relations by using Poisson bracket : $\{A,B\} \rightarrow \frac{1}{ih}[A,B]$.

(I am not totally familiar with the quantization process I just started to learn QFT so I may have said mistakes, but the important is you understand globally my question).

My question is: is the process of quantization a deep postulate or are there some theories that explain why this process works?

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  • $\begingroup$ Just to be clear: there aren't many interacting QFTs which are well-defined as quantum mechanical theories. High-Energy physics QFTs are mostly looked at as perturbative theories, and their success is justified by the accuracy of their predictions, not by postulates. Or are you asking about QM in general? $\endgroup$ – Solenodon Paradoxus Apr 20 '17 at 0:25
  • $\begingroup$ The links given explains why different quantization methods give the same results. I am asking if there is any theory explaining why we should associate an operator to a classical scalar ? Is it only because it fits very well the experiments ? @Solenodon Paradoxus hmmm I am asking why in general the process of quantization works in QM. I am not familiar at all with interacting QFT to know what to answer precisely to this question. You can consider I am talking about the free field for example. $\endgroup$ – StarBucK Apr 20 '17 at 9:35

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