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When quantizing a classical field theory, e.g. Klein-Gordon theory, the Hilbert space of one-particle states is taken to be a set of equivalence classes of (Lebesgue) measurable and square integrable solutions of the classical field equation, but how do you use the classical theory to construct operators on this Hilbert space?
I asked that question in a different way here (in the Topology & Geometry forum), but got no replies, so I'm trying again here.
I asked that question in a different way here (in the Topology & Geometry forum), but got no replies, so I'm trying again here.