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I tried to calculate the Amplitude of the external leg correction of figure 6.1 in Peskin&Schroeder.

I focus on the diagram with one incomming charged fermion $f^-$ (with momentum $p'$), then a loop with a virtual photon (integrating over momentum $k$). After this a vertex with an emmitting photon (momentum q) and the outgouning fermion $f^-$ with momentum $p$. Momentum conservation says $q=p'-p$

My problem is: When I write the propagator of the fermion $f^-$ between the loop and the emission of the photon, its momentum is well known $p'$ and on-shell and therefore the propagator has a infrared divergenz. An other divergenz which can be handled with Pauli-Villars regularisation comes from the loop.

Is this correct so far? How to handle the divergenz comming from the on-shell propagator?

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  • $\begingroup$ Note that, whether or not actual homework, this question is homework-like since it just asks for the way to carry out a calculation, and is thus likely off-topic under the homework policy. $\endgroup$ – ACuriousMind Feb 26 '15 at 17:53
  • $\begingroup$ This is a question to a general problem. I only mentioned this case as an example to illustrate what I was wondering about. $\endgroup$ – Matthias Feb 26 '15 at 19:38

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