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Plyushchay, Mikhail S.

Nonlinear supersymmetry as a hidden symmetry. (English) Zbl 1427.81043

Kuru, Şengül (ed.) et al., Integrability, supersymmetry and coherent states. A volume in honour of Professor Véronique Hussin. In part selected contributions from the 6th international workshop on new challenges in quantum mechanics: integrability and supersymmetry, Valladolid, Spain, June 27–30, 2017. Cham: Springer. CRM Ser. Math. Phys., 163-186 (2019).
Summary: 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 \(\mathcal{PT} \)-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.
For the entire collection see [Zbl 1421.81004].

Cited in 3 Documents

MSC:

81Q60 Supersymmetry and quantum mechanics
35Q55 NLS equations (nonlinear Schrödinger equations)

Keywords:

hidden symmetry; exotic supersymmetry; nonlinear superconformal symmetry; reflectionless and finite-gap systems; perfect invisibility
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Full Text: DOI arXiv

References:

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