  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 the electromagnetic
coupling alpha. For the explicit example of scattering in a plane wave
background, we compare QED with classical electrodynamics in the limit h-bar
goes to zero, finding agreement with the Lorentz-Abraham-Dirac and
Landau-Lifshitz equations, and with Larmor's formula. The first quantum
corrections are also presented.
