Poincare covariant mechanics on noncommutative space

TL;DR

This paper develops a Poincare covariant framework for mechanics on noncommutative space, demonstrating how relativistic invariance can be maintained and exploring the effects on particle dynamics and electromagnetic interactions.

Contribution

It introduces a relativistically invariant noncommutative particle model coupled to electromagnetic fields using Dirac's constrained systems approach.

Findings

Poincare invariance leads to deformation of the noncommutative algebra.

Deformation effects persist in the nonrelativistic limit.

The approach extends the Dirac method to noncommutative relativistic systems.

Abstract

The Dirac approach to constrained systems can be adapted to construct relativistic invariant theories on a noncommutative (NC) space. As an example, we propose and discuss relativistic invariant NC particle coupled to electromagnetic field by means of the standard term $A^\mu\dot x_\mu$. Poincare invariance implies deformation of the free particle NC algebra in the interaction theory. The corresponding corrections survive in the nonrelativistic limit.