Abstract
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.
Highlights
We derive radiation reaction from QED in a strong background field
For answers one would like to turn to QED, and the natural place to look for radiation reaction (‘RR’) is in photon emission from particles accelerated by background fields
This has lead to confusion over which Feynman diagrams do/do not contain RR, and it has even been claimed that QED and classical electrodynamics are not compatible [6, 14]
Summary
This first section is intended to be pedagogical, since understanding the physics here will help when comparing classical and quantum results, and is enough to answer question ‘1)’ in the introduction. Radiation field F1 sourced by x0, i.e. by a particle moving under the Lorentz force. To compare directly with QED, it is helpful to go back to the classical equations of motion and solve them perturbatively (rather than eliminating the radiation field to obtain LAD), in such a way that RR effects appear as corrections to the Lorentz force. The particle’s orbit is corrected due to the term F1 x0, i.e. by the fact that the particle has emitted the radiation F1; this is radiation reaction. It appears at order e2 in the electron’s motion, as expected. Recoil effects appear in the radiated energy first at order e4, through the F1F3 ∼ j0 j2 cross term
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