Physical systems in a space with noncommutativity of coordinates

Abstract

We consider a space with canonical noncommutativity of coordinates. The problem of rotational symmetry breaking is studied in this space. To preserve the rotational symmetry we consider the generalization of constant matrix of noncommutativity to a tensor defined with the help of additional coordinates governed by a rotationally symmetric system. The properties of physical systems are examined in the rotationally invariant space with noncommutativity of coordinates. Namely, we consider an effect of coordinate noncommutativity on the energy levels of the hydrogen atom in the rotationally invariant noncommutative space. The motion of a particle in the uniform field is also studied in the noncommutative space with preserved rotational symmetry. On the basis of exact calculations we show that there is an effect of coordinate noncommutativity on the mass of a particle and conclude that noncommutativity causes the anisotropy of mass.