Michael Kiessling, Rutgers University

Abstract

Physics folklore says that a classical point charge, when accelerated by some electromagnetic field, produces electromagnetic radiation through which it loses energy and momentum to the field degrees of freedom. Many physicists (in particular: Abraham, Lorentz, Dirac, Landau and Lifshitz, ...) tried to compute the associated `radiation-reaction' force on the point charge. Alas, all proposals so far failed the litmus test: their fomulas produce a vanishing radiation-reaction when a point charge is accelerated by a uniform electric field (such as occurs between the plates of a charged capacitor). Recently I combined ideas of Poincare' and of Bopp, Lande'-Thomas, and Podolsky, and managed to compute the exact expression for the radiation-reaction force in a classical electrodynamics model. Jointly with Shadi Tahvildar-Zadeh we also proved local well-posedness of the joint initial-value problem for fields and point charges. Since the self-force expression is very complicated, MAPLE was then used to study the motion of a point charge accelerated by a constant electric field. Radiation-reaction effects showed very clearly and dramatically: unexpectedly, a dynamical phase transition was found. Subsequently a proof of this dynamical scenario was supplied. I will explain all this without getting into the nitty-gritty of the technical details.