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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) http://prola.aps.org/abstract/PR/v140/i2B/pB397_1

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relevant books.google.com/… –  pcr Nov 14 '11 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

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interesting! thanks, I'll take a look at it soon –  pcr Nov 14 '11 at 16:16
    
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. –  pcr Nov 14 '11 at 20:22
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