Interesting Q someone asked: quantum electrodynamics has an obvious classical theory it corresponds to, but quantum chromodynamics and electroweak theory don’t—why’s that? Possible answer: there’s electromagnetism in daily life, but no strong or electroweak force
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The uniqueness of the lagrangian, wholesale, is what I had in mind! Weinberg and friends made arguments for example about the uniqueness of GR’s lagrangian and that for other fields (conditional of course on the exclusion of things like higher derivatives)
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Yea, i think it's a super interesting question. The restriction to being gauge symmetric and Renormalizable + Poincare invariant really restricts what you can write down.
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Kinda curious what kind of observable we could find in a non-perturbative QFT that doesn't have a Lagrangian. Maybe something from QCD?
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consider the operator e^(-1/φ^2)
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i’m a physicist and this is still total gibberish to me

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that's because you study big things that go boom .. we study little things that go boop
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"Modulo gauge symmetries" as in symmetries through transformations by some given integer multiple of some, say, n?
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No, modulo just means "divided out" in this sense .. really it just means "ignoring"
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