The relativistic dynamics of the combined particle-field system in nonlinear renormalized electrodynamics
Hans-Peter Gittel, Jerzy Kijowski, and Eberhard Zeidler
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Submission date: 25. Mar. 1997
published in: Communications in mathematical physics, 198 (1998) 3, p. 711-736
DOI number (of the published article): 10.1007/s002200050492
with the following different title: The relativistic dynamics of the combined particle-field system in renormalized classical electrodynamics
This paper develops a general theory for the nonlinear interaction between a charged particle and an electromagnetic field. For the combined particle-field system, a fundamental relativistically invariant equation of motion is derived from first principles. This fundamental equation was first obtained in an alternative way by Kijowski in an earlier paper. It can be proved that the initial-value problem for the particle-field system is well-posed. The existence and uniqueness result is based on a careful analysis of the singularites of the electromagnetic field along the trajectory of the moving charged particle. Furthermore, the Banach fixed-point principle is used. This new theory improves the classical Dirac theory for the motion of electrons. In particular, it is shown how to exclude the Dirac paradox of runaway solutions having overlight speed.