Gauge invariance and classical dynamics of noncommutative particle theory

TL;DR

This paper investigates the classical dynamics of noncommutative particles in electromagnetic fields, establishing gauge invariance and analyzing motion in magnetic fields within Hamiltonian and Lagrangian frameworks.

Contribution

It introduces generalized gauge transformations for noncommutative particles and explores their classical equations of motion in external electromagnetic fields.

Findings

Existence of generalized gauge transformations

Detailed analysis of particle motion in constant magnetic fields

Formulation of classical dynamics in Hamiltonian and Lagrangian form

Abstract

We consider a model of classical noncommutative particle in an external electromagnetic field. For this model, we prove the existence of generalized gauge transformations. Classical dynamics in Hamiltonian and Lagrangian form is discussed, in particular, the motion in the constant magnetic field is studied in detail.