``Charge-Dyon" System As The Reduced Oscillator

TL;DR

This paper demonstrates that the Kustaanheimo-Stiefel transformation reduces a 4D oscillator to an integrable system describing a charged particle interacting with a dyon, revealing new insights into such interactions.

Contribution

It shows that the Kustaanheimo-Stiefel transformation leads to an integrable system modeling charge-dyon interactions, extending previous understanding of oscillator reductions.

Findings

Reduction yields an integrable charge-dyon system

Transformation connects oscillator dynamics with electromagnetic interactions

Provides a new approach to studying charge-monopole systems

Abstract

It is shown, that in the general case the Kustaanheimo-Stiefel transformation (reduction of $4d$ oscillator on the twistor space by the Hamiltonian action of $U(1)$ with further time-reparametrization) leads to the integrable system, describing the interaction of a spinless electrically charged particle with a dyon .