Motion of charged particle in a class of homogeneous spaces

TL;DR

This paper investigates the dynamics of charged particles within a broad class of homogeneous spaces, focusing on the influence of electromagnetic fields and metric deformations on particle trajectories.

Contribution

It introduces a general framework for analyzing charged particle motion in homogeneous spaces with deformed metrics, extending previous models to more complex geometries.

Findings

Derived equations of motion for charged particles in these spaces.

Characterized the impact of metric deformations on particle trajectories.

Provided explicit descriptions for special cases like homogeneous Riemannian spaces.

Abstract

We study the motion of charged particle under a natural choice of electromagnetic field in a general class of compact homogeneous spaces. As a special case we describe the motion in homogeneous Riemannian spaces $(G/H,g)$, where $g$ is any deformation of a normal metric along the fibers of a homogeneous fibration $K/H\rightarrow G/H \rightarrow G/K$.