ar X iv : h ep - t h / 04 07 24 7 v 1 2 8 Ju l 2 00 4 N = 2 SUPERSYMMETRIC PLANAR PARTICLES AND MAGNETIC INTERACTION FROM NONCOMMUTATIVITY

We describe a N=2 supersymmetric extension of the nonrelativistic (2+1)-dimensional model describing particles on the noncommutative plane with scalar (electric) and vector (magnetic) interactions. First, we employ the N = 2 superfield technique and show that in the presence of a scalar N = 2 superpotential the magnetic interaction is implied by the presence of noncommutativity of position variables. Further, by expressing the supersymmetric Hamiltonian as a bilinear in N = 2 supercharges we obtain two supersymmetric models with electromagnetic interactions and two different noncanonical symplectic structures describing noncommutativity. We show that both models are related by a map of the Seiberg-Witten type.