Twisted acceleration-enlarged Newton-Hooke space-times and conservative force terms

TL;DR

This paper investigates classical systems on twist-deformed acceleration-enlarged Newton-Hooke space-times, showing that only canonical twist deformation preserves the conservativeness of force terms in these models.

Contribution

It demonstrates that among various twist deformations, only canonical twist deformation maintains conservative force terms in classical particle and oscillator models.

Findings

Force terms are conservative only under canonical twist deformation.

Noncommutativity affects force conservativeness in the models.

Analysis of classical systems on noncommutative space-times.

Abstract

There are analyzed two classical systems defined on twist-deformed acceleration-enlarged Newton-Hooke space-times - nonrelativistic particle moving in constant field force $\vec{F}$ and harmonic oscillator model. It is demonstrated that only in the case of canonical twist deformation the force terms generated by space-time noncommutativity remain conservative for both models.