Classical Radiation Reaction Off-Shell Corrections to the Covariant Lorentz Force

Abstract

It has been shown by Gupta and Padmanabhan that the radiation reaction force of the Abraham-Lorentz-Dirac equation can be obtained by a coordinate transformation from the inertial frame of an accelerating charged particle to that of the laboratory. We show that the problem may be formulated in a flat space of five dimensions, with five corresponding gauge fields in the framework of the classical version of a fully gauge covariant form of the Stueckelberg- Feynman-Schwinger covariant mechanics (the zero mode fields of the 0,1,2,3 components correspond to the Maxwell fields). Without additional constraints, the particles and fields are not confined to their mass shells. We show that in the mass-shell limit, the generalized Lorentz force obtained by means of the retarded Green's functions for the five-dimensional field equations provides the classical Abraham-Lorentz-Dirac radiation reaction terms (with renormalized mass and charge). We also obtain general coupled equations for the orbit and the off-shell dynamical mass during the evolution. The theory does not admit radiation if the particle remains identically on-shell. The structure of the equations implies that the mass-shell deviaiton is bounded when the external field is removed.

Plain TeX, 12 pages

References in corpus (1)

• Radiation from a charged particle and radiation reaction -- revisited

Cited by in corpus (4)

• Green Functions For Wave Propagation on a 5D manifold and the Associated Gauge Fields Generated by a Uniformly Moving Point Source
• Gravitational Repulsion within a Black-Hole using the Stueckelberg Quantum Formalism
• Eikonal Approximation to 5D Wave Equations as Geodesic Motion in a Curved 4D Spacetime
• On the Green-Functions of the classical offshell electrodynamics under the manifestly covariant relativistic dynamics of Stueckelberg