Diagrams / Self-energy with VP insertion

Self-energy with VP insertion

Perturbative order$\alpha^{2}$
Topologyrainbow
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

The one-loop electron self-energy (rainbow) with a vacuum polarization bubble inserted into the virtual photon line. Two vertices on the main fermion line, two on the internal fermion loop. Factorizes as the product of the rainbow topology and the bubble topology, but is 1PI and contributes independently at two loops.