N=2 Supersymmetric Planar Particles and Magnetic Interaction from Noncommutativity
arXiv:hep-th/0407247 · doi:10.1016/j.physletb.2004.10.013
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.
LaTeX,12 pages.Minor corrections; version appears in PLB
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