Features of free particles system motion in noncommutative phase space and conservation of the total momentum

Abstract

Influence of noncommutativity on the motion of composite system is studied in noncommutative phase space of canonical type. A system composed by N free particles is examined. We show that because of the momentum noncommutativity free particles of different masses with the same velocities at the initial moment of time do not move together. The trajectory and the velocity of a free particle in noncommutative phase space depend on its mass. So, a system of the free particles flies away. Also, it is shown that the total momentum defined in the traditional way is not integral of motion in a space with noncommutativity of coordinates and noncommutativity of momenta. We find that in the case when parameters of noncommutativity corresponding to a particle are determined by its mass, the trajectory and the velocity of the free particles are independent of the mass. Also, the total momenta as integrals of motion can be introduced in noncommutative phase space.