Deformed Chern–Simons interaction for nonrelativistic point particles

We deform the interaction between nonrelativistic point particles on a plane and a Chern–Simons field to obtain an action invariant with respect to time-dependent area-preserving diffeomorphisms. The deformed and undeformed Lagrangians are connected by a point transformation leading to a classical Seiberg–Witten map between the corresponding gauge fields. The Schrödinger equation derived by means of Moyal–Weyl quantization from the effective two-particle interaction exhibits