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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Replying to @litgenstein
There definitely is a classical Lagrangian for those theories. It’s just that quantum effects are very important in the presence of confinement and SSB, not so much when everything’s perturbative.
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Replying to @seanmcarroll
Good stuff! Do you think the classical lagrangian is unique? Or that it depends on how you take the classical limit?
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Replying to @litgenstein @seanmcarroll
In non perturbative QFTs there actually exist observables for which we don't have Lagrangians .. Do you mean unique modulo gauge symmetries & conserved global symmetries? Even the Dirac equation gives the same physics depending on if you use +-m
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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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