Noether symmetries for charged particle motion under a magnetic monopole and general electric fields

摘要

The search for Noether point symmetries for non-relativistic charged particlemotion is reduced to the solution for a set of two coupled, linear partialdifferential equations for the electromagnetic field. These equations arecompletely solved when the magnetic field is produced by a fixed magneticmonopole. The result is applied to central electric field cases, in particularto the time-dependent monopole-oscillator problem. As an additional example ofthe theory, we found all Noether point symmetries and invariants for a constantmagnetic field and a time-dependent harmonic electric field with a forcingterm.