  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.
