N=2 Supersymmetric Planar Particles and Magnetic Interaction from Noncommutativity

TL;DR

This paper develops an N=2 supersymmetric model for particles on a noncommutative plane, revealing how noncommutativity induces magnetic interactions and relating two models via a Seiberg-Witten map.

Contribution

It introduces a novel N=2 supersymmetric extension of noncommutative planar particles, linking electromagnetic interactions with noncommutativity through superfield techniques.

Findings

Magnetic interaction arises from noncommutativity in the model.

Two supersymmetric models with different symplectic structures are constructed.

The models are connected by a Seiberg-Witten type map.

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.