Izvestiya of Saratov University.


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Ivanov E. A. Superextensions of Landau Models. Izvestiya of Sarat. Univ. 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.

  1. Landau L. Diamagnetismus der Metalle // Z. Phys. 1930. Vol.64. P.629.
  2. Haldane F.D.M. Fractional Quantization of the Hall Effect: A Hierarchy of Incompressible Quantum Fluid States // Phys. Rev. Lett. 1983. Vol.51. P.605. 
  3. Quantum Hall Effects: Field Theoretical Approach and Related Topics, Singapour: World Scientific, 2000. 
  4. Ivanov E. Supersymmetrizing Landau models // Theor. Math. Phys. 2008. Vol.154. P.349.
  5. Ivanov E., Mezincescu L., Townsend P.K. Fuzzy CP("|/w) as a quantum superspace. Preprint UB-ECM-PF-03/31, Univer-sitat de Barcelona; arxiv: hep-th/031 1 159. 
  6. vanov E., Mezincescu L, Townsend P.K. A super-flag Landau model. Preprint UB-ECM-PF-04/08, Universitat de Barcelona; arxiv: hep-th/0404108. 
  7. Hasebe K, Kimura Y. Fuzzy supersphere and supermonopole // Nucl. Phys. B. 2005. Vol.709. P.94 . 
  8. Ivanov E., Mezincescu L, Townsend P. K. Planar superLandau models // JHEP. 2006. Vol.0601. P.143.
  9. Curtright Т., Ivanov E., Mezincescu L., Townsend P.K. Planar super-Landau models revisited // JHEP. 2007. Vol.0704. P.020. 
  10. Hasebe K. Quantum Hall liquid on a noncommutative superplane//Phys. Rev. D. 2005. Vol.72. P.105017. 
  11. Bender C. Introduction to /Т-symmetric quantum symmetry // Contemp. Phys. 2005. Vol.46. P.277-292. 
  12. Bender C. Making sense of non-Hermitian Hamiltonians // Rept. Prog. Phys. 2007. Vol.70. P.947. 
  13. Curtright Т., Mezincescu L. Biorthogonal quantum systems // J. Math. Phys. 2007. Vol.48. P.092106. 
  14. Beylin A., Curtright Т., Ivanov E., Mezincescu L., Townsend P.K. Unitary Spherical Super-Landau Models // JHEP. 2008. Vol.0810. P.069.
  15. Elvang H., Polchinski J. The Quantum Hall Effect on R4 II Preprint NSF-ITP-02-120, University of California; arxiv: hepth/0209104.
  16. Madore J. The fuzzy sphere // Class. Quant. Grav. 1992. Vol.9. P.69. 
  17. Witten E. Dynamical breaking of supersymmetry // Nucl. Phys. B. 1981. Vol.188. P.513. 
  18. Akulov V.P., Pashnev A.I. Supersymmetric quantum mechanics and spontaneous breaking of supersymmetry at the quantum level // Theor. Math. Phys.1985. Vol.65. P.1027. 
  19. Volkov D. V., Pashnev A.I. Supersymmetric Lagrangian for particles in proper time // Theor. Math. Phys. 1980. Vol.44. P.770. 
  20. Robert D., Smilga A.V. Supersymmetry vs ghosts // J. Math. Phys. 2008. Vol.49. P.042104.