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
I think what Sean is saying is that the Classical theory *is* the QCD lagrangian at tree level
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so when everything is weakly coupled (as he said), everything is well defined and we can calculate the observables using tree level interactions of Yang Mills, just as we can with QED at tree level as well.. it's just that the theory breaks down at ~.1GeV
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