Exact trajectories of charged particles in the Dirac monopole field

TL;DR

This paper derives exact trajectories for charged particles influenced by a Dirac monopole, extending Noether's theorem to magnetic systems and explicitly solving the equations of motion.

Contribution

It provides the first explicit integration of particle trajectories in a Dirac monopole field using an extended Noether's theorem.

Findings

Explicit formulas for particle trajectories in monopole fields

Extension of Noether's theorem to magnetic forces

Analytical solutions to equations of motion

Abstract

We consider the motion of charged particles in the presence of a Dirac magnetic monopole. We use an extension of Noether's theorem for systems with magnetic forces and integrate explicitly the equations of motion.