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
Certainly not for QCD; adding GGdual changes the quantum theory but not the classical one. In general there is no 1-to-1 or onto map from quantum to classical theories or back.
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To add to this, the reason this doesn't show up classically is because GGdual is a total derivative, and so doesn't effect Euler Lagrange equations
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