TY - JOUR

T1 - Radiation reaction of the classical off-shell relativistic charged particle

AU - Oron, O.

AU - Horwitz, L. P.

PY - 2001/6

Y1 - 2001/6

N2 - 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 generalised Lorentz force obtained by means of the retarded Green's functions for the five dimensional field equations provides the classical Ahraham-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 as well as an autonomous non-linear equation of third order for the off-shell mass. The theory does not admit radiation if the particle does not move off-shell. The structure of the equations implies that mass-shell deviation is bounded when the external field is removed.

AB - 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 generalised Lorentz force obtained by means of the retarded Green's functions for the five dimensional field equations provides the classical Ahraham-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 as well as an autonomous non-linear equation of third order for the off-shell mass. The theory does not admit radiation if the particle does not move off-shell. The structure of the equations implies that mass-shell deviation is bounded when the external field is removed.

UR - http://www.scopus.com/inward/record.url?scp=0035647197&partnerID=8YFLogxK

U2 - 10.1023/A:1017564002246

DO - 10.1023/A:1017564002246

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AN - SCOPUS:0035647197

SN - 0015-9018

VL - 31

SP - 951

EP - 966

JO - Foundations of Physics

JF - Foundations of Physics

IS - 6

ER -