Photon propagator

$\gamma \to \gamma$

The vacuum polarization tensor $\Pi^{\mu\nu}(q^2)$: the sum of all 1PI corrections to the photon propagator. The Ward identity forces it to be transverse, determined by a single scalar function $\Pi(q^2)$. Source of the running of $\alpha$ and the Uehling potential in hydrogen.

Tree-level diagrams

1 diagram.

Order $\alpha$ diagrams

2 diagrams.