Generating of additional force terms in Newton equation by twist-deformed Hopf algebras and classical symmetries

TL;DR

This paper compares two methods of generating force terms in nonrelativistic particle models, one using twist-deformed quantum space-times and the other classical symmetries, identifying conditions for their equivalence.

Contribution

It introduces a comparison between quantum deformation and classical symmetry approaches to force generation in nonrelativistic models.

Findings

Both approaches can produce identical force terms under specific conditions.

Conditions for equivalence depend on the deformation parameters and symmetry transformations.

The study bridges quantum algebraic methods with classical symmetry analysis in physics.

Abstract

We compare two ways of force terms generating in the model of nonrelativistic particle moving in the presence of constant field force $\vec{F}$. First of them uses the twist-deformed acceleration-enlarged Newton-Hooke quantum space-times while the second one incorporates the doubly enlarged Newton-Hooke transformations of classical space. Particulary, we find the conditions for which the both treatments provide the same force terms.