Role of momentum and velocity for radiating electrons

Radiation reaction remains one of the most fascinating open questions in electrodynamics. The development of multi-petawatt laser facilities capable of reaching extreme intensities has leant this topic a new urgency, and it is now more important than ever to properly understand it. Two models of radiation reaction, due to Landau and Lifshitz and to Sokolov, have gained prominence, but there has been little work exploring the relation between the two. We show that in the Sokolov theory electromagnetic fields induce a Lorentz transformation between momentum and velocity, which eliminates some of the counterintuitive results of Landau-Lifshitz. In particular, the Lorentz boost in a constant electric field causes the particle to lose electrostatic potential energy more rapidly than it otherwise would, explaining the long-standing mystery of how an electron can radiate while experience no radiation reaction force. These ideas are illustrated in examples of relevance to astrophysics and laser-particle interactions, where radiation reaction effects are particularly prominent.