(2+1)-dimensional models with a Chern-Simons-like term and noncommutative geometry

We consider new D = 2 nonrelativistic model of classical mechanics providin g via the Noether theorem the (2 + 1)-Galilean symmetry algebra with two ce ntral charges: the mass m and the coupling constant k of a Chern-Simons-lik e term. We discuss the interpretation of k as describing the noncommutativi ty of D = 2 space coordinates. We quantize the model and show that it descr ibes the superposition of a free motion in noncommutative D = 2 space as we ll as the "internal" oscillator modes. We add a suitably chosen class of ve locity-dependent two-particle interactions, which is described by local pot entials in D = 2 noncommutative space. We show that the indefinite metric d ue to the third-order time derivative term in the field equations, even in the presence of interactions, can be eliminated by the imposition of a subs idiary condition.