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Register a new userOn the Green-Functions of the classical offshell electrodynamics under the manifestly covariant relativistic dynamics of Stueckelberg
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In previous paper derivations of the Green function have been given for 5D off-shell electrodynamics in the framework of the manifestly covariant relativistic dynamics of Stueckelberg (with invariant evolution parameter $tau$). In this paper, we reconcile these derivations resulting in different explicit forms, and relate our results to the conventional fundamental solutions of linear 5D wave equations published in the mathematical literature. We give physical arguments for the choice of the Green function retarded in the fifth variable $tau$.
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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.
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