Radiation reaction in strong field QED

We derive radiation reaction from QED in a strong background field. We identify, in general, the diagrams and processes contributing to recoil effects in the average momentum of a scattered electron, using perturbation theory in the Furry picture: we work to lowest nontrivial order in α. For the explicit example of scattering in a plane wave background, we compare QED with classical electrodynamics in the limit ℏ→0, finding agreement with the Lorentz-Abraham-Dirac and Landau-Lifshitz equations, and with Larmorʼs formula. The first quantum corrections are also presented.