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Nonlinear Supersymmetry as a Hidden Symmetry

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Integrability, Supersymmetry and Coherent States

Part of the book series: CRM Series in Mathematical Physics ((CRM))

Abstract

Nonlinear supersymmetry is characterized by supercharges to be higher order in bosonic momenta of a system, and thus has a nature of a hidden symmetry. We review some aspects of nonlinear supersymmetry and related to it exotic supersymmetry and nonlinear superconformal symmetry. Examples of reflectionless, finite-gap and perfectly invisible \(\mathcal {P}\mathcal {T}\)-symmetric zero-gap systems, as well as rational deformations of the quantum harmonic oscillator and conformal mechanics, are considered, in which such symmetries are realized.

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Acknowledgements

Financial support from research projects Convenio Marco Universidades del Estado (Project USA1555) and FONDECYT Project 1190842, Chile, and MINECO (Project MTM2014-57129-C2-1-P), Spain, is acknowledged.

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  1. Departamento de Física, Universidad de Santiago de Chile, Casilla, Santiago, Chile

    Mikhail S. Plyushchay

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  1. Mikhail S. Plyushchay
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Correspondence to Mikhail S. Plyushchay .

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  1. Department of Physics, Ankara University, Ankara, Turkey

    Şengül Kuru

  2. Department of Theoretical Physics, Atomic Physics and Optics, University of Valladolid, Valladolid, Spain

    Javier Negro

  3. Department of Theoretical Physics, Atomic Physics and Optics, University of Valladolid, Valladolid, Spain

    Luis M. Nieto

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Plyushchay, M.S. (2019). Nonlinear Supersymmetry as a Hidden Symmetry. In: Kuru, Ş., Negro, J., Nieto, L. (eds) Integrability, Supersymmetry and Coherent States. CRM Series in Mathematical Physics. Springer, Cham. https://doi.org/10.1007/978-3-030-20087-9_6

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