On the classical $\kappa$-particle

TL;DR

This paper investigates how velocity depends on momentum for a free massive particle within the framework of $ppa$-Poincare9 symmetry, revealing a monotonic relationship with an upper velocity limit of 1.

Contribution

It provides a calculation of velocity-momentum dependence for $ppa$-Poincare9 symmetric particles using non-commuting space-time coordinates, highlighting its monotonic nature.

Findings

Velocity dependence is monotonic.

Maximum velocity approaches the speed of light.

Velocity has an upper limit of 1.

Abstract

The dependence of velocity on momentum for the free massive particle obeying the $\kappa $-Poincar\'{e} Poisson symmetry is calculated in terms of intrinsic non-commuting space-time coordinates and shown to have a monotonic character, with upper limit of velocity equal to 1.