Can anyone give an mathematical elaboration of the following statement:
Quantization is a functor carrying the category of Hilbert space and linear maps to that of Symplectic manifolds satisfying some conditions specified by laws of Physics.
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1Related: http://mathoverflow.net/q/6200 and http://mathoverflow.net/q/8606 – Qmechanic May 25 '13 at 09:23
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1where is that statement taken from? – Prathyush May 25 '13 at 13:41
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10That's not quantization. The direction is backwards. – user1504 May 25 '13 at 16:05
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1See also Geometric Quantization, and a article by John Baez – Trimok May 27 '13 at 10:20
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1See also Bates and Weinstein – Trimok May 27 '13 at 10:33
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1possible duplicate of (a superposition of) Why quantum mechanics? and What is quantization?. I think the answers by Urs Schreibers address this question quite well. – Danu Dec 25 '14 at 15:15
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Quantization is *not a functor*; second quantization is, trivially. – Cosmas Zachos Dec 04 '21 at 17:49