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I'm interested in the (very) low energy limit of quantum electrodynamics. I've seen that taking this limit does not yield Maxwell equations, but a quantum corrected non-linear version of them.

  1. If quantum phenomena are responsible for what we see in the macroscipic world, it is expected that there is a limit which does lead to Maxwell equations from QED? how should I think of this limit?
  2. A classical theory of strong and weak interactions is not physically meaningful. Is this a direct consequence that these fields are (unlike electrodynamics) mediated by short-range interactions? Kindly prove or disprove.
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The quantum corrections are generally only significant for wavelengths comparable to the compton wavelength of the electron, or at intensities where pair-production is significant, if you're talking about the Euler-Heisenberg correction. The low energy limit of QED is Maxwell's equations for ordinary purposes. –  Ron Maimon Jun 5 '12 at 1:33
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