I've just posted a new paper to the ArXiv, "Classical states, quantum field measurement", which comes out of a math bender I've been on for about the last month. I'll be coming out of that, hopefully. When I'm in that state, ideas come and go so fast that I lose track of them, but almost all of them turn out to be nonsense, so there's really no need to keep track. I make so many mistakes, I've seen ideas I've thought absolutely solid crash and burn because of sign errors, or conceptual misunderstandings, or really anything that can go wrong, that I now always prefix anything with "if I haven't made any mistakes". Sometimes I only realize after a few years what every physicist knows. But this paper feels a little different. Something really dropped out that's simple enough (in a mathematician's sense of simple), just a few lines, the whole paper's only 4 pages, that if I've made a mistake there's not many places for it to hide. Either on Saturday or Sunday, so this is really much too soon to feel confident, I tried something and it worked spectacularly.

So what does this paper do? One of the problems in trying to understand quantum field theory is that "quantized Dirac spinor fields" (otherwise called "fermion fields", they're what we use to describe matter in contrast to electromagnetism) are a lot different from classical physics. This paper kinda fixes that, it makes fermion fields look almost as classical as a 19th Century physicist could wish it to be. Not quite, because one doesn't and one doesn't want to get rid of 90 years of history, but if physicists understand it and I've made not too many mistakes, and hopefully no big mistakes, there'll be some change.

So what does this paper do? Enough of the hand waving! The things (operators) that come out of a Dirac field that correspond to what we can measure are the constituents of what is called a Lie algebra; there are other operators that don't correspond to anything we can measure, a bigger algebra that is the heart of what is a lot different about fermion fields, but they're so necessary to the way the theory is constructed that they've really been thought part of the whole package. This paper introduces a new way to construct the same Lie algebra of observables, but using different, almost, very nearly, really all but classical tools to do it. Once a mathematician sees the few lines that set this up, and if they also accept the embedding of the Lie algebra of observables into the new big Lie algebra, really a whole lot becomes possible. Even if it comes to nothing, there's something about having a new perspective that makes everything never the same again. In the light of the new bigger algebra, that old bigger algebra looks a lot more sensible.

I doubt anyone here will want it, but I can't give a link to the paper on the ArXiv until this evening. The abstract is

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.

so that's fun. [Added September 21st, https://arxiv.org/abs/1709.06711.]