Graduate QED vs Scalar QED: Proving Divergence in P&S 10.1

[Higgsy]

In Peskin and Schroeder problem 10.1 is about showing that superficially divergent diagrams that would destroy gauge invariance converge or vanish. We are supposed to prove it for the 1-photon, 3-photon, and 4-photon vertex diagrams. Does this change for scalar QED?

 

[vanhees71]

If this is a homework question, please post it in the homework forum.

Some hints: To show that proper verices with an odd number of external photon lines only, use the charge-conjugation invariance of QED, which holds for both spinor and scalar QED. For the four-photon vertex, use the corresponding Ward-Takahashi identity to show that it is finite at any loop order. Note that you have to combine all diagrams at a given order before you to the integrals to make this explicit for concrete examples of diagrams!