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Ivanov E. A. Superextensions of Landau Models. Izvestiya of Saratov University. Physics , 2010, vol. 10, iss. 1, pp. 24-35. DOI: 10.18500/1817-3020-2010-10-1-24-35

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Superextensions of Landau Models

Ivanov Evgeny Alexeevich, Joint Institute for Nuclear Research

The paper is a review of recent works on superextensions of the model of non-relativistic quantum charged particle moving in a homogeneous magnetic field on the plane R2 (Landau model), and a model of the particle in the field of Dirac monopole on the sphere S2: SU(2)11/(1) (Haldane model). We consider the models on the supersphere Sl/(2|1)/l/(1|1), superflag SU(2|1)/[l/(1)xl/(1)] and their planar limits, based upon a geometric interpretation of these models and their bosonic proptotypes as d=1 analogs of nonlinear sigma models of the Wess-Zumino-Novikov-Witten type. While quantizing supersymmetric models, there arise states with the negative norms and, in order to overcome this difficulty, it proves necessary to introduce a non-trivial metrics on the Hilbert space of quantum states. A characteristic feature of the planar models is the presence of hidden dynamical N=2 worldline supersymmetry.

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