2023/12/16 by Hadad, Yaron, Kaminer, Ido, Elitzur, Avshalom +1
#Classical Physics (physics.class-ph) #FOS: Physical sciences #Mathematical Physics (math-ph)
paper · doi:10.48550/arxiv.2312.10367
This paper revisits the geometric foundations of electromagnetic theory, by studying Faraday's concept of field lines. We introduce "covariant electromagnetic field lines," a novel construct that extends traditional field line concepts to a covariant framework. Our work includes the derivation of a closed-form formula for the field line curvature in proximity to a moving electric charge, showcasing the curvature is always non-singular, including nearby a point charge. Our geometric framework leads to a geometric derivation of the Lorentz force equation and its first-order corrections, circumventing the challenges of self-force singularities and providing insights into the problem of radiation-reaction. This study not only provides a fresh geometric perspective on electromagnetic field lines but also opens avenues for future research in fields like quantum electrodynamics, gravitational field theory, and beyond.