On the uniform motion of a relativistic charged particle in a homogeneous electromagnetic field in Minkowski space E24

摘要

We discuss the geometric characterization of the trajectory of a moving charged particle, for the case of a homogeneous electromagnetic field, in Minkowski space E24 when the motion is governed by the Lorentz equation. We employ a totally relativistic approach during the discussion. It is based on a systematic use of the Faraday antisymmetric tensor properties of the electromagnetic field and of the four-dimensional Frenet-Serret formula, which is adapted to the Minkowski 4-space with index two to determine the worldline geometry of the electromagnetic field acting on the particle. Finally, we present the necessary and sufficient conditions to obtain uniform motion of the relativistic charged particle in a homogeneous electromagnetic field in E24.