Supersymmetrizing landau models

摘要

We review recent progress in constructing and studying superextensions of the Landau problem of a quantum particle on a plane in a uniform magnetic field and also its Haldane S(2)supercript stop generalization. We focus on the planar super Landau models that are invariant under the inhomogeneous supergroup ISU (1 vertical bar 1), a contraction of the supergroup SU(2 vertical bar 1), and are minimal superextensions of the original Landau model. Their significant common feature is the presence of a hidden dynamical worldline N= 2 supersymmetry, which exists at both the classical and quantum levels and is revealed most naturally in passing to the new invariant inner products in the space of quantum states in order to make the norms of all states positive. For one of the planar models, the superplane Landau model, we present an off-shell worldline superfield formulation in which the N = 2 supersymmetry becomes explicit.