Composite system in rotationally invariant noncommutative phase space

TL;DR

This paper explores the properties of composite systems in a rotationally invariant noncommutative phase space, deriving conditions for algebraic consistency and analyzing energy level corrections in two-particle Coulomb systems, including exotic atoms.

Contribution

It establishes conditions under which noncommutative algebra applies to composite systems and derives energy corrections for Coulomb systems in this framework.

Findings

Coordinates in noncommutative space are mass-independent and kinematic.

Momenta are proportional to mass, consistent with classical mechanics.

Energy levels of Coulomb systems receive calculable corrections due to noncommutativity.

Abstract

Composite system is studied in noncommutative phase space with preserved rotational symmetry. We find conditions on the parameters of noncommutativity on which commutation relations for coordinates and momenta of the center-of-mass of composite system reproduce noncommutative algebra for coordinates and momenta of individual particles. Also, on the conditions the coordinates and the momenta of the center-of-mass satisfy noncommutative algebra with effective parameters of noncommutativity which depend on the total mass of the system and do not depend on its composition. Besides, it is shown that on these conditions the coordinates in noncommutative space do not depend on mass and can be considered as kinematic variables, the momenta are proportional to mass as it has to be. A two-particle system with Coulomb interaction is studied and the corrections to the energy levels of the system are found in rotationally invariant noncommutative phase space. On the basis of this result the effect of noncommutativity on the spectrum of exotic atoms is analyzed.