Basic observables for the accelerated electron and its field

• Published in: arXiv.org
• Main Author: Dondera, Mihai
• Format: Paper Journal Article
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 06.11.2018
• Subjects: Angular momentum; Covariance; Dirac equation; Electromagnetic fields; Electromagnetism; Electrons; Equations of motion; Physics - Classical Physics; Physics - High Energy Physics - Theory; Singularities
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.1811.03001

We revisit in the framework of the classical theory the problem of the accelerated motion of an electron, taking into account the effect of the radiation emission. We present results for the momentum and energy of the electromagnetic field of an accelerated electron for a spatial region excluding a vicinity of the electron and a procedure to compensate their singularities in the limit of the point electron. From them we infer expressions for the observables momentum and energy of the electron. They lead, together with those corresponding to the emitted radiation, to an equation of motion of the electron that coincides, in the case of an external electromagnetic field, with the Lorentz-Dirac equation. Based on the results for the linear momentum and using the same calculation method, we obtain the equations corresponding to the angular momentum of the electron and its field. While the formalism used is not wholly manifestly covariant, arguments based on relativistic covariance are invoked and used at appropriate places, where they play an essential role.