Past exam of the advanced quantum field theory for particle physics course of the University of Oxford / 2020 / 1 / iv / Solution

With $q=p^{\prime }-p$ and the routing just described, multiplication of the three QED Feynman rules for the Feynman vertices, the two Dirac propagators and the photon propagator gives $(-i{e}_D{)}^3{i}^2(-i)=-e_D^3$. Hence the unrenormalized amputated Feynman vertex through this order isFor the renormalized Feynman vertex, add $-i{e}_D{\delta }_1{\gamma }^{\mu }$ to this expression. Contributions from replacing parameters inside the one-loop term by their bare counterparts enter at higher loop order.