Kartik Prabhu
I am not sure what “the problem of quantization” is!? If we are given a non-relativistic theory, we do not ask whether a unique “relativization” of the theory exists. Similarly, we do not ask for a unique “general relativization” of Newtonian gravity. We also do not ask for a “moleculization” of Navier-Stokes equations to “derive” that water is made up of discrete molecules. Usually, these are questions phrased in the reverse order, i.e., “how to get a non-relativistic or continuum” limit in certain special situations from a more fundamental theory. So why is one asking for the existence and uniqueness of the “quantization” of some classical phase space?
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