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On p.576 in Peskin & Schroeder, he argues that for a photon propagator with almost on-shell momentum connecting two parts as depicted in the Feynman diagram below, that one can replace the metric in the propagator with the polarisation sum $-g^{\mu\nu}=\sum_i\epsilon^\mu_i\epsilon^{\nu\ast}_i-\epsilon^\mu_+\epsilon^{\nu\ast}_--\epsilon^\mu_-\epsilon^{\nu\ast}_+$. He goes on, then the terms with the unphysical polarisations $\epsilon_\pm$ vanish by the Ward identity.

Feynman diagram

However, as recently discussed in one of my previous questions about the Ward identity (see here), processes like $e^-\rightarrow e^-\gamma$ are unphysical and therefore the Ward identity does not apply to them.

So, how to salvage the argumentation of P&S? Do the terms vanish anyway but for another reason? Or is there another detail I oversaw, that makes the Ward identity still applicable?

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