 Tree-level Compton amplitude

For a charged Dirac particle, incoming momenta $p,k$ and outgoing momenta $p^{\prime },k^{\prime }$ obey $p+k=p^{\prime }+k^{\prime }$. The two QED diagrams have internal fermion momenta $p+k$ and $p-k^{\prime }$, giving $s$ and $u$ channels. The amplitude is proportional to $\bar{u}(p^{\prime })[/{ϵ}^{\prime \ast }R(p+k)/ϵ+/ϵR(p-k^{\prime })/{ϵ}^{\prime \ast }]u(p)$, where $R(q)=(/q+m)/(q^2-m^2+i0)$. It is related to particle-antiparticle two-photon annihilation by crossing symmetry, with appropriate changes to external wavefunctions and conjugations.