Hyperbolic Motion in the Finite-size Model of the Radiating Electron

Abstract

Within the framework of the finite-size model of the electron recently dovelopped the case of hyperbolic motion is studied rigorously by means of an exact solution. The energy-momentum balance is discussed as well as the critical phenomena arising if the external field strength comes into the range of order of the maximal self-field strength of the particle. It is found that the commonly accepted Lorentz-Dirac-Rohrlich theory is only a good approximation for small values of the external field strength. I. What is the Problem?There are numerous treatises in the literature, which try to overcome the infinities of the classical point-like electron by resorting to a non-linear generalization of Maxwell's electrodynamics*. The leading idea standing behind these attempts is the conjecture that Maxwell's linear theory is valid only in some distance of the center of the particle, where the field strength is sufficiently small. But in the immediate neighbourhood of the singularity of the linear theory the field strength should become so strong that the nonlinearities are dominating and are forcing down the field strength to a finite value in the center of the electron.As an example consider the so-called "Rosenparticle" in scalar classical field theory 2 . The field equation in the static, spherical symmetric case is which has as a particular, "particle-like" solution 4> = Z-(Z*g + r 2 )-ih .(1,2)Clearly, the quantityis a characteristic linear dimension of the particle described by (1,2), and in the limit r0-+ 0 one obtains Poisson's equation for the point-electron ~-r/r -r,m jNow it is a well-known fact that non-linear theories are extremely difficult to handle with, not only as far as quantization is concerned but also with respect to the classical interaction with other particles or "external" fields. In order to get an impression what sort of phenomena arise in the classical theory as a lowest-order approximation to the nonlinearity effect, we have constructed a covariant Unauthenticated Download Date | 5/13/18 5:43 AM