An Introduction To Quantum Field Theory - M. Peskin, D. Schroeder (Perseus, 1995) · Problem 10.1
Systematics of Renormalization — M. Peskin, D. Schroeder (Perseus, 1995)
Physics — QFT · qed-renormalization-one-loop
Problem
10.1 One-loop structure of QED. In Section 10.1 we argued from general principles that the photon one-point and three-point functions vanish, while the four-point function is finite.
(a) Verify directly that the one-loop diagram contributing to the one-point function vanishes. There are two Feynman diagrams contributing to the three-point function at one-loop order. Show that these cancel. Show that the diagrams contributing to any n-point photon amplitude, for n odd, cancel in pairs.
(b) The photon four-point amplitude is a sum of six diagrams. Show explicitly that the potential logarithmic divergences of these diagrams cancel.