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Schwinger has on his grave (it seems) the relation between the g-factor of the electron and the fine structure constant:

$g = 2 \ + \ \alpha / \pi \ + \ ... $

Did Schwinger or somebody else ever give a simple explanation for the second term of the right hand side? The 2 appears from Dirac's equation. The second term is due to the emission and absorption of a photon. Is there a simple way to see that this process leads to the expression alpha/pi?

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This is a loop integral which is done elegantly in Weinberg, Schwinger's way. This is as simple as it gets. – Ron Maimon Jul 18 '12 at 18:08
Also see chapter 6 of Peskin. – DJBunk Jul 18 '12 at 18:34

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