Nonlinear realizations, the orbit method and Kohn's theorem

TL;DR

This paper applies the orbit method to analyze the center of mass motion of charged particles in a magnetic field with harmonic confinement, revealing nonlinear symmetry actions and comparing different geometric approaches.

Contribution

It introduces a novel application of the orbit method to this physical system and compares nonlinear symmetry realizations with Eisenhart lift techniques.

Findings

Identifies nonlinear symmetry actions on phase space.

Connects orbit method with Eisenhart lift in this context.

Provides insights into the geometric structure of the system.

Abstract

The orbit method is used to describe the centre of mass motion of the system of particles with fixed charge to mass ratio moving in homogeneous magnetic field and confined by harmonic potential. The nonlinear action of symmetry group on phase space is identified and compared with the one obtained with the help of Eisenhart lift.