Classical states, quantum field measurement

Question

Referee this paper: arXiv:1709.06711 by Peter Morgan

Please use comments to point to previous work in this direction, and reviews to referee the accuracy of the paper. Feel free to edit this submission to summarise the paper (just click on edit, your summary will then appear under the horizontal line)

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Additionally to the abstract on the paper itself, the following:

  Fairly formally, I construct the Lie algebra of globally U(1) invariant observables of the free quantized Dirac spinor field, call it D, starting from a commuting raising and lowering algebra, call it B (instead of the usual process of starting from an anti-commuting raising and lowering algebra, call it F). So we have D⊂B as well as the usual D⊂F. Something of a surprise that this is possible, even more that it takes only a few lines in the notation I use, but once that's done the usual vacuum state over D, which of course has an extension over F, can also be extended to act over B (here, trivially), with the resulting state having properties that to me seem striking. The more-or-less classicality that emerges is the least of the transformation of how we can think about fermion fields.
  I will mention that the notation I use in the paper might be offputtingly novel, however it has a moderately principled motivation as the use of intrinsic vector methods in the test function space (which for free fields is equipped with a pre-inner product), which I have found and I commend it to you as a very rewarding way to think about quantum field theory.