Exact solution of the EM radiation-reaction problem for classical finite-size and Lorentzian charged particles

• Published in: European physical journal plus Vol. 126; no. 4; p. 42
• Main Authors: Cremaschini, C., Tessarotto, M.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer-Verlag 01.04.2011; Springer Nature B.V
• Subjects: Applied and Technical Physics; Atomic; Charge distribution; Charged particles; Complex Systems; Condensed Matter Physics; Divergence; Dynamical systems; Electrodynamics; Exact solutions; Existence theorems; Mathematical analysis; Mathematical and Computational Physics; Molecular; Optical and Plasma Physics; Particle size; Physics; Physics and Astronomy; Principles; Radiation; Regular Article; Relativity; Representations; Tensors; Theoretical; Uniqueness theorems; Mass Current Density; Thomas Precession; Hamilton Variational Principle; Lorentz Boost; Classical Dynamical System
• ISSN: 2190-5444; 2190-5444
• DOI: 10.1140/epjp/i2011-11042-8

. An exact solution is given to the classical electromagnetic (EM) radiation-reaction (RR) problem, originally posed by Lorentz. This refers to the dynamics of classical non-rotating and quasi-rigid finite-size particles subject to an external prescribed EM field. A variational formulation of the problem is presented. It is shown that a covariant representation for the EM potential of the self-field generated by the extended charge can be uniquely determined, consistent with the principles of classical electrodynamics and relativity. By construction, the retarded self-4-potential does not possess any divergence, contrary to the case of point charges. As a fundamental consequence, based on the Hamilton variational principle, an exact representation is obtained for the relativistic equation describing the dynamics of a finite-size charged particle (RR equation), which is shown to be realized by a second-order delay-type ODE. Such equation is proved to apply also to the treatment of Lorentzian particles, i.e. , point-masses with finite-size charge distributions, and to recover the usual LAD equation in a suitable asymptotic approximation. Remarkably, the RR equation admits both standard Lagrangian and conservative forms, expressed, respectively, in terms of a non-local effective Lagrangian and a stress-energy tensor. Finally, consistent with the Newton principle of determinacy, it is proved that the corresponding initial-value problem admits a local existence and uniqueness theorem, namely it defines a classical dynamical system.