Multi-particle systems in quantum spacetime and a novel challenge for center-of-mass motion

TL;DR

This paper investigates the kinematics of multi-particle systems in quantum spacetime, highlighting the importance of defining total momentum linearly and revealing subtle effects on center-of-mass motion in $$-Minkowski spacetime.

Contribution

It advocates for using the standard linear sum of momenta for multiparticle systems and uncovers subtle effects on center-of-mass motion in quantum spacetime.

Findings

Total momentum should be defined as the linear sum of particle momenta.

Subtle effects on center-of-mass motion due to constituent properties.

Comparison of different total momentum definitions in $$-Minkowski spacetime.

Abstract

In recent times there has been considerable interest in scenarios for quantum gravity in which particle kinematics is affected nonlinearly by the Planck scale, with encouraging results for the phenomenological prospects, but also some concerns that the nonlinearities might produce pathological properties for composite/multiparticle systems. We here focus on kinematics in the $\kappa$-Minkowski noncommutative spacetime, the quantum spacetime which has been most studied from this perspective, and compare the implications of the alternative descriptions of the total momentum of a multiparticle system which have been so far proposed. We provide evidence suggesting that priority should be given to defining the total momentum as the standard linear sum of the momenta of the particles composing the system. We also uncover a previously unnoticed feature concerning some (minute but conceptually important) effects on center-of-mass motion due to properties of the motion of the constituents relative to the center of mass.