I wonder if there is an intuitive way to obtain the $\frac{\alpha}{2\pi}$ correction to electron's $\frac12 (g-2)$ just like how Bethe estimated the Lamb shift?
Here is an attempt by Drell & Pagels (dispersion relation) Link
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$\begingroup$ relevant books.google.com/… $\endgroup$– pcrNov 14, 2011 at 3:54
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T. Welton gave an estimation in 1948. It was of good order of magnitude but of the opposite sign, apparently, because his estimations were non-relativistic and did not take into account virtual pairs. https://docs.google.com/open?id=0B4Db4rFq72mLOTE4ZTQ0NzUtMzZmNy00ZDU1LTgwNDQtMjU4NDUwMDAyMDg0
answered Nov 14, 2011 at 10:43
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$\begingroup$ about the nonrelativistic concern: Drell&Pagels also included NR estimate and they got the sign correct. Another possibility is that somehow the magnetic correction reduces the electron mass. $\endgroup$– pcrNov 14, 2011 at 20:22