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?