v3 of "Classical States, Quantum Field Measurement"

I've posted a new version of https://arxiv.org/abs/1709.06711 to the arXiv. Much has changed, not least the addition of "Appendix A: Classical mechanics to quantum mechanics: poissonification". We've lived with quantization as the way of getting from classical physics to quantum physics for 90 years, but poissonification is different, in particular because the Correspondence Principle doesn't apply, which changes a lot of how we might think about Quantum Mechanics in future. [Naming things can be a awkward business: poissonization is already used for something rather different.]
Really crucial is the recognition that classical measurement (in the Hamiltonian formalism) is not just about functions on phase space, it is also about eigenvalues of operators that generate transformations, which are constructed using the Poisson bracket (especially see the Zalamea reference) and which generate a non-commutative algebra of operators.

What is not said about the paper in its abstract is that it demystifies QM by constructing a way in which we can take quantum fields to be classical random fields —effectively to be a sophisticated classical signal processing formalism—, which dissolves the Measurement Problem (insofar as classical statistical physics does not itself have a measurement problem) and makes superposition and entanglement classically natural, at the cost of a limited nonlocality that is already implicit in QM whenever we use state projection operators.
What has to be admitted, however, is that whereas the construction for the electromagnetic field is quite straightforward, and even its interpretation seems fairly clear cut, for the quantized Dirac spinor case not so much. The construction is OK as far as it goes, but there are constraints in the Dirac case for which I'd say I do not have an adequate account.

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https://arxiv.org/abs/1709.06711
From: Peter Morgan
Date: Wed, 20 Sep 2017 03:35:27 GMT   (8kb)
Date (revised v2): Fri, 29 Sep 2017 17:47:29 GMT   (12kb)
Date (revised v3): Mon, 29 Jan 2018 19:25:56 GMT   (20kb)

Title: Classical states, quantum field measurement
Authors: Peter Morgan
Categories: quant-ph hep-th math-ph math.MP
Comments: v3: 13 pages. Reorganized. v2: 6 pages. Additional calculations
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
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  The Hilbert spaces of the quantized electromagnetic field and of the quantized Dirac spinor field are constructed using classical random fields acting on a vacuum state, allowing a classical interpretation of the states of the respective quantum theories. For the quantized Dirac spinor field, the Lie algebra 𝓓 of global-U(1) invariant observables can be constructed as a subalgebra of a bosonic raising and lowering algebra, 𝓓⊂𝓑, and the usual vacuum state over 𝓓 can be extended (here, trivially) to act over 𝓑.
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