Radiation-reaction in classical offshell electrodynamics: I. The above mass-shell case

TL;DR

This paper investigates radiation reaction in offshell electrodynamics, revealing that the mass deviation scalar either stabilizes to zero or diverges, with no runaway motion and potential chaotic behavior in divergent cases.

Contribution

It provides a detailed numerical analysis of radiation reaction for above-mass-shell particles in offshell electrodynamics, including stability and chaos insights.

Findings

Mass deviation scalar $$ either decays to zero or diverges.

No runaway solutions are observed in the system.

Chaotic behavior may occur in divergent cases.

Abstract

Offshell electrodynamics based on a manifestly covariant off-shell relativistic dynamics of Stueckelberg, Horwitz and Piron, is five-dimensional. In this paper, we study the problem of radiation reaction of a particle in motion in this framework. In particular, the case of above-mass-shell is studied in detail, where the renormalization of the Lorentz force leads to a system of non-linear differential equations for 3 Lorentz scalars. The system is then solved numerically, where it is shown that the mass-shell deviation scalar $\ve$ either smoothly falls down to 0 (this result provides a mechanism for the mass stability of the off-shell theory), or strongly diverges under more extreme conditions. In both cases, no runaway motion is observed. Stability analysis indicates that the system seems to have chaotic behavior in the divergent case. It is also shown that, although a motion under which the mass-shell deviation $\ve$ is constant but not-zero, is indeed possible, but, it is unstable, and eventually it either decays to 0 or diverges.