Supersymmetrizing Landau models |
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Authors: | E A Ivanov |
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Institution: | (1) Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Dubna, Moscow Oblast, Russia |
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Abstract: | 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 S2 generalization. We focus on the planar super Landau models that are invariant under the inhomogeneous supergroup ISU (1|1),
a contraction of the supergroup SU(2|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.
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 154, No. 3, pp. 409–423, March, 2008. |
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Keywords: | supersymmetry superfield supergroup particle |
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