Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 1 (2005), 012, 10 pages      math-ph/0511075

Radiation Reaction, Renormalization and Poincaré Symmetry

Yurij Yaremko
Institute for Condensed Matter Physics of National Academy of Sciences of Ukraine, 1 Svientsitskii Str., Lviv, 79011 Ukraine

Received July 08, 2005, in final form October 23, 2005; Published online November 01, 2005

We consider the self-action problem in classical electrodynamics of a massive point-like charge, as well as of a massless one. A consistent regularization procedure is proposed, which exploits the symmetry properties of the theory. The radiation reaction forces in both 4D and 6D are derived. It is demonstrated that the Poincaré-invariant six-dimensional electrodynamics of the massive charge is renormalizable theory. Unlike the massive case, the rates of radiated energy-momentum tend to infinity whenever the source is accelerated. The external electromagnetic fields, which do not change the velocity of the particle, admit only its presence within the interaction area. The effective equation of motion is the equation for eigenvalues and eigenvectors of the electromagnetic tensor. The interference part of energy-momentum radiated by two massive point charges arbitrarily moving in flat spacetime is evaluated. It is shown that the sum of work done by Lorentz forces of charges acting on one another exhausts the effect of combination of outgoing electromagnetic waves generated by the charges.

Key words: classical electrodynamics; point-like charges; Poincaré invariance; conservation laws; renormalization procedure.

pdf (223 kb)   ps (170 kb)   tex (47 kb)


  1. Kosyakov B.P., Exact solutions of classical electrodynamics and the Yang-Mills-Wong theory in even-dimensional spacetime, Teor. Mat. Fiz., 1999, V.119, N 1, 119-135 (English transl.: Theor. Math. Phys., 1999, V.119, N 1, 493-509), for revised version see hep-th/0207217.
  2. Nesterenko V.V., Curvature and torsion of the world curve in the action of the relativistic particle, J. Math. Phys., 1991, V.32, N 12, 3315-3320.
  3. Rohrlich F., Classical charged particles, Redwood City, Addison-Wesley, 1990.
  4. Teitelboim C., Splitting of the Maxwell tensor: radiation reaction without advanced fields, Phys. Rev. D, 1970, V.1, N 6, 1572-1582.
  5. Yaremko Yu., On the validity of the Lorentz-Dirac equation, J. Phys. A: Math. Gen., 2002, V.35, 831-839; Corrigendum, J. Phys. A: Math. Gen., 2003, V.36, 5159.
  6. Yaremko Yu., On the regularization procedure in classical electrodynamics, J. Phys. A: Math. Gen., 2003, V.36, 5149-5156.
  7. Kosyakov B.P., On the inert properties of particles in classical theory, 2003, Fiz. Elem. Chast. i Atom. Yadra, V.34, 1564 (English transl.: Phys. Part. Nucl., 2003, V.34, 808), hep-th/0208035.
  8. Dirac P.A.M., Classical theory of radiating electrons, Proc. R. Soc. A, 1938, V.167, 148-169.
  9. Aguirregabiria J.M., Bel L., Electromagnetic energy and linear momentum radiated by two point charges, Phys. Rev. D, 1984, V.29, N 6, 1099-1106.
  10. Yaremko Yu., Interference in the radiation of two point-like sources, J. Phys. A: Math. Gen., 2004, V.37, L531-L538.
  11. Yaremko Yu., Interference of outgoing electromagnetic waves generated by two point-like sources, Int. J. Mod. Phys. A, 2005, V.20, N 1, 129-159.
  12. Yaremko Yu., Radiation reaction, renormalization and conservation laws in six-dimensional classical electrodynamics, J. Phys. A: Math. Gen., 2004, V.37, 1079-1091.
  13. Yaremko Yu., Radiation reaction and renormalization via conservation laws of the Poincaré group, J. Phys. Stud., 2004, V.8, N 3, 203-210.
  14. Kazinski P.O., Sharapov A.A., Radiation reaction for a massless charged particle, Class. Quantum Grav., 2003, V.20, 2715-2725.
  15. Brink L., Deser S., Zumino B., Di Vecchia P., Howe P., Local supersymmetry for spinning particles, Phys. Lett. B, 1976, V.64, N 4, 435-438.
  16. Rylov Yu.A., The algebraical structure of the electromagnetic tensor and description of charged particles moving in the strong electromagnetic field, J. Math. Phys., 1989, V.30, N 2, 521-536.
  17. Fushchich W.I., Nikitin A.G., Symmetry of equations of quantum mechanics, Moscow, Nauka, 1990 (in Russian).

Previous article   Next article   Contents of Volume 1 (2005)