N=2 Supersymmetric Planar Particles and Magnetic Interaction from Noncommutativity

Abstract

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.