Covariant electromagnetic field lines

[摘要] Faraday introduced electric field lines as a powerful tool for understanding the electric force, and these field lines are still used today in classrooms and textbooks teaching the basics of electromagnetism within the electrostatic limit. However, despite attempts at generalizing this concept beyond the electrostatic limit, such a fully relativistic field line theory still appears to be missing. In this work, we propose such a theory and define covariant electromagnetic field lines that naturally extend electric field lines to relativistic systems and general electromagnetic fields. We derive a closed-form formula for the field lines curvature in the vicinity of a charge, and show that it is related to the world line of the charge. This demonstrates how the kinematics of a charge can be derived from the geometry of the electromagnetic field lines. Such a theory may also provide new tools in modeling and analyzing electromagnetic phenomena, and may entail new insights regarding long-standing problems such as radiation-reaction and self-force. In particular, the electromagnetic field lines curvature has the attractive property of being non-singular everywhere, thus eliminating all self-field singularities without using renormalization techniques.

[发布机构] Department of Mathematics, University of Arizona, Tucson; AZ; 85721, United States^1;H.H. Wills Physics Laboratory, University of Bristol, Tyndall Avenue, Bristol; BS8 1TL, United Kingdom^2;Department of Physics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge; MA; 02139, United States^3;Iyar, Israeli Institute for Advanced Research, POB 651, Zichron Ya'akov; 3095303, Israel^4

[效力级别] 力学 [学科分类] 力学，机械学

[关键词] Closed-form formulae;Electric field lines;Electromagnetic phenomena;Electrostatic limits;Radiation reactions;Relativistic systems;Renormalization;Standing problems