Features of description of composite system's motion in twist-deformed space-time

Abstract

Composite system made of $N$ particles is considered in twist-deformed space-time. It is shown that in the space the motion of the center-of-mass of the system depends on the relative motion. Influence of deformation on the motion of the center-of-mass of composite system is less than on the motion of individual particles and depends on the system's composition. We conclude that if we consider commutation relations for coordinates of a particle to be proportional inversely to its mass, the commutation relations for coordinates of composite system do not depend on its composition and are proportional inversely to system's total mass, besides the motion of the center-of-mass is independent of the relative motion. In addition we find that inverse proportionality of parameters of noncommutativity to mass is important for considering coordinates in twist-deformed space as kinematic variables and for preserving of the weak equivalence principle.