 Solution

The third panel of the figure in part a is a representative four-photon box diagram. Fix the external photon labelled 1 and orient the fermion loop. The six inequivalent cyclic orders of the labelled interaction vertices areThey are obtained by permuting labels $2,3,4$ on the displayed box, keeping label 1 fixed. Equivalently there are three undirected boxes, each with two opposite fermion flows. The reversal pairs areFor four photon interaction vertices, the sign in part d is positive, so the members of each pair add. They can be represented by three box diagrams multiplied by two. There is no tree photon self-coupling in QED, and therefore no triangle or bubble with a photon self-vertex to add at this loop order. This is the one-loop light-by-light scattering contribution, of order $e^4$.