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Classical electrodynamics gives strange results when considering a moving charge in its self generated field (Abraham-Lorentz equation).

Some 50 years ago there were many efforts and publications about how to interpret those results, including works of Dirac and other prominent physicists.

My question is, whether these peculiarities are removed by the formalism of field quantization (QED). I have read that it is the case, but other sources state the opposite, so it seems to be controversial.

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  • $\begingroup$ The title refers to infinite self-energy, while the body refers to back-reaction. Clearly these are related problems, but you might want to clarify in the body. When you say "it seems to be controversial," it might be helpful to point us to some sources that advocate the different points of view. $\endgroup$ – Ben Crowell Jan 17 at 18:39
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No, in QED the main term of the self-action diverges and it is discarded, just like in CED.

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    $\begingroup$ I don't think "just like in CED" is correct. In classical electrodynamics, we simply lack a self-consistent theory of point charges, and there is no method that works for discarding the infinity. $\endgroup$ – Ben Crowell Jan 17 at 18:38
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    $\begingroup$ There is the work of Epstein and Glaser, which showed how to not get these infinities in the first place. Sadly i only found this very short wikipedia article on it: en.wikipedia.org/wiki/Causal_perturbation_theory $\endgroup$ – Lorenz Mayer Jan 17 at 19:13
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    $\begingroup$ @LorenzMayer: A "normal" or physically correct theory does need that "causal" perturbation theory by Epstein and Glaser. $\endgroup$ – Vladimir Kalitvianski Jan 17 at 19:24
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    $\begingroup$ There are at least two editions of Scharf's book on "Finite QED" based on E&G approach, but I do not like their trick. $\endgroup$ – Vladimir Kalitvianski Jan 17 at 19:41

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