The hidden geometry of electromagnetism
arXiv:1503.01150 · doi:10.1088/1742-6596/626/1/012024
Abstract
Nearly all field theories suffer from singularities when particles are introduced. This is true in both classical and quantum physics. Classical field singularities result in the notorious self-force problem, where it is unknown how the dynamics of a particle change when the particle interacts with its own (self) field. Self-force is a pressing issue and an active research topic in gravitational phenomena, as well as a source of controversies in classical electromagnetism. In this work, we study a hidden geometrical structure manifested by the electromagnetic field-lines that has the potential of eliminating all singularities from classical electrodynamics. We explore preliminary results towards a consistent way of treating both self- and external fields.
9 pages, 3 figures. This is a preprint for the proceedings of DICE2014 in Tuscany, Italy