A QED vs. Scalar QED

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1. Apr 5, 2016

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?

2. Apr 6, 2016

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!