Noncommutative relativistic particle on the electromagnetic background

TL;DR

This paper introduces a noncommutative relativistic particle model interacting with electromagnetic fields, featuring a gauge-invariant action with a variable noncommutativity parameter, and explores its Poincare symmetry and coupling properties.

Contribution

It proposes a novel noncommutative relativistic particle framework with a variable noncommutativity parameter and constructs its consistent electromagnetic coupling.

Findings

The model maintains Poincare invariance with a gauge-fixed noncommutativity parameter.

A consistent coupling to electromagnetic fields is achieved.

The gauge-fixed formulation explicitly displays the noncommutativity parameter.

Abstract

Noncommutative version of D-dimensional relativistic particle is proposed. We consider the particle interacting with the configuration space variable $\theta^{\mu\nu}(\tau)$ instead of the numerical matrix. The corresponding Poincare invariant action has a local symmetry, which allows one to impose the gauge $\theta^{0i}=0, ~ \theta^{ij}=const$. The matrix $\theta^{ij}$ turns out to be the noncommutativity parameter of the gauge fixed formulation. Poincare transformations of the gauge fixed formulation are presented in the manifest form. Consistent coupling of NC relativistic particle to the electromagnetic field is constructed and discussed.