Dynamics in the magnetic/dual magnetic monopole

TL;DR

This paper explores complex three-dimensional dynamical systems with gauge symmetries, focusing on a charged particle interacting with magnetic and dual monopoles, revealing new geometric and physical insights.

Contribution

It introduces a novel class of 3D systems with non-commuting variables using the Lagrange-Souriau formalism, extending planar models to three dimensions with gauge symmetries.

Findings

Analysis of motion and conservation laws in the monopole system

Identification of geometric and gauge symmetries in 3D dynamics

Proposals for physical realizations of the theoretical model

Abstract

Inspired by the geometrical methods allowing the introduction of mechanical systems confined in the plane and endowed with exotic galilean symmetry, we resort to the Lagrange-Souriau 2-form formalism, in order to look for a wide class of 3D systems, involving not commuting and/or not canonical variables, but possessing geometric as well gauge symmetries in position and momenta space too. As a paradigmatic example, a charged particle simultaneously interacting with a magnetic monopole and a dual monopole in momenta space is considered. The main features of the motions, conservation laws and the analogies with the planar case are discussed. Possible physical realizations of the model are proposed.