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A derivation is here: http://en.wikipedia.org/wiki/Lamb_shift#Derivation or in Landau-Lifshitz. Bethe's original derivation is found e.g. in Matt Schwartz's Harvard lecture here http://isites.harvard.edu/fs/docs/icb.topic792163.files/20-LambShift.pdf The leading contribution to the Lamb shift is the one-loop level (the first non-classical ...

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