# Classical states, quantum field measurement

Peter Morgan
September 19, 2017
Manifestly Lorentz covariant representations of the algebras of the quantized electromagnetic field and of the observables of the quantized Dirac spinor field are constructed that act on Hilbert spaces that are generated using classical random fields acting on a vacuum state, allowing a comparatively classical interpretation of the states of the theory. 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.

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