I think I have found a mistake/wrong formulation at Peskin’s, when he discusses the renormalization of QED.(adsbygoogle = window.adsbygoogle || []).push({});

In particular, he defines the 1PI of the electron’s self-energy on page 331 as: [itex] –i\Sigma( \displaystyle{\not}p ) [/itex] and the corresponding counterterm on page 332 as: [itex] i( \displaystyle{\not}p \delta_2 - \delta_m ) [/itex]. It is then logical to assume that the combined term can be written in 1-loop order as:

[tex] –i\Sigma( \displaystyle{\not}p ) = –i

\Sigma_2( \displaystyle{\not}p ) + i( \displaystyle{\not}p \delta_2-\delta_m ) [/tex]

Then if one uses the on-shell renormalization conditions (pg. 332):

[tex] \Sigma ( \displaystyle{\not}p = m) = 0 [/tex]

[tex] \frac{d}{d\displaystyle{\not}p} \Sigma( \displaystyle{\not}p )\bigg|_{\displaystyle{\not}p = m} = 0

[/tex]

they yield the counterterms:

[tex] \delta_2 = \frac{d}{d\displaystyle{\not}p }\Sigma_2( \displaystyle{\not}p ) \bigg|_{\displaystyle{\not}p = m} [/tex] and

[tex] \delta_m = -\Sigma_2(m) +m \delta_2 [/tex]

Peskin claims though that: [tex] \delta_m = -\Sigma_2(m) [/tex]

I implore you to share any insights on the matter, cause this triviality is driving me crazy!

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# QED renormalization in Peskin's

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