= Ultraviolet pole of the QED vertex
{title2=$\Lambda^\mu_{\rm UV}=e^2\gamma^\mu/(16\pi^2\epsilon)$}
Write the <QED> vertex as $-ie(\gamma^\mu+\Lambda^\mu)$. In <Feynman gauge> and $d=4-2\epsilon$, the one-loop <ultraviolet pole> has the local form $\Lambda^\mu_{\rm UV}=e^2\gamma^\mu/(16\pi^2\epsilon)$. Its coefficient follows from the large-<momentum> <gamma matrices> contraction $\gamma^\alpha\not k\gamma^\mu\not k\gamma_\alpha\mapsto(d-2)^2k^2\gamma^\mu/d$. It is independent of external kinematics, whereas the full finite vertex requires additional structures <off shell>. Its cancellation verifies the <Ward identity for QED renormalization constants>.
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