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TMF, 2008, Volume 154, Number 3, Pages 409–423 (Mi tmf6179)  

This article is cited in 13 scientific papers (total in 13 papers)

Supersymmetrizing Landau models

E. A. Ivanov

Joint Institute for Nuclear Research, Bogoliubov Laboratory of Theoretical Physics

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 $S^2$ 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 $\mathcal N=2$ 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 $\mathcal N=2$ supersymmetry becomes explicit.

Keywords: supersymmetry, superfield, supergroup, particle

DOI: https://doi.org/10.4213/tmf6179

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English version:
Theoretical and Mathematical Physics, 2008, 154:3, 349–361

Bibliographic databases:


Citation: E. A. Ivanov, “Supersymmetrizing Landau models”, TMF, 154:3 (2008), 409–423; Theoret. and Math. Phys., 154:3 (2008), 349–361

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Hasebe K., “Hyperbolic supersymmetric quantum Hall effect”, Phys. Rev. D, 78:12 (2008), 125024, 13 pp.  crossref  mathscinet  adsnasa  isi  elib  scopus
    2. Beylin A., Curtright T.L., Ivanov E., Mezincescu L., Townsend P.K., “Unitary spherical super-Landau models”, J. High Energy Phys., 2008, no. 10, 069, 46 pp.  crossref  mathscinet  zmath  isi  scopus
    3. Ben Geloun J., Govaerts J., Scholtz F.G., “The $\mathscr N=1$ supersymmetric Landau problem and its supersymmetric Landau level projections: the $\mathscr N=1$ supersymmetric Moyal-Voros superplane”, J. Phys. A, 42:49 (2009), 495203, 18 pp.  crossref  mathscinet  zmath  adsnasa  isi  scopus
    4. Ivanov E., Niederle J., “Biharmonic superspace for $N=4$ mechanics”, Phys. Rev. D, 80:6 (2009), 065027, 23 pp.  crossref  mathscinet  adsnasa  isi  elib  scopus
    5. Ivanov E., Konyushikhin M., “N=4, 3D supersymmetric quantum mechanics in a non-Abelian monopole background”, Phys. Rev. D, 82:8 (2010), 085014, 8 pp.  crossref  adsnasa  isi  elib  scopus
    6. Beylin A., Curtright T., Ivanov E., Mezincescu L., “Generalized $\mathscr N=2$ super Landau models”, J. High Energy Phys., 2010, no. 4, 091, 27 pp.  crossref  mathscinet  zmath  isi  elib  scopus
    7. Hasebe K., “Supersymmetric quantum hall liquid with a deformed supersymmetry”, Phys. Atomic Nuclei, 73:2 (2010), 345–351  crossref  adsnasa  isi  elib  scopus
    8. Ivanov E.A., “Super-Landau models: unitarity and hidden symmetries”, Phys. Atomic Nuclei, 73:2 (2010), 352–358  crossref  adsnasa  isi  elib  scopus
    9. Ivanov E.A., “Generalized Landau Models with N=2 Worldline Supersymmetry”, Phys. Atom. Nuclei, 75:10 (2012), 1227–1233  crossref  adsnasa  isi  elib  scopus
    10. Bychkov V., Ivanov E., “N=4 Supersymmetric Landau Models”, Nucl. Phys. B, 863:1 (2012), 33–64  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    11. V. S. Bychkov, E. A. Ivanov, “The $\mathcal N{=}4$ super Landau models”, Theoret. and Math. Phys., 174:1 (2013), 40–51  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    12. Goykhman M., Ivanov E., Sidorov S., “Super Landau Models on Odd Cosets”, Phys. Rev. D, 87:2 (2013), 025026  crossref  mathscinet  adsnasa  isi  scopus
    13. Ivanov E.A., “Gauge fields, nonlinear realizations, supersymmetry”, Phys. Part. Nuclei, 47:4 (2016), 508–539  crossref  isi  elib  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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