Diagrams / Nested rainbow

Nested rainbow

Perturbative order$\alpha^{2}$
Topologynested
Symmetry factorCounts overcounting in the perturbation series. If a diagram has internal symmetries—ways to relabel internal lines and get the same diagram back—the symmetry factor divides that out. Most QED diagrams have S=1; the vacuum polarization bubble has S=1/2 because swapping the two internal fermion lines gives the same diagram.1.0
Divergence UV divergent IR divergent
Gauge invariant aloneNo

Contributes to

Electron propagator

Two virtual photons emitted and reabsorbed by the electron, one enclosed inside the other. Four vertices on the main fermion line with pairing $(v_1,v_4)(v_2,v_3)$: the outer photon spans the full diagram while the inner photon is contained within it.