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arXiv · 1007.1962

Self-isospectrality, mirror symmetry, and exotic nonlinear supersymmetry

Mikhail S. Plyushchay·Luis-Miguel Nieto
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Abstract

We study supersymmetry of a self-isospectral one-gap Poschl-Teller system in the light of a mirror symmetry that is based on spatial and shift reflections. The revealed exotic, partially broken nonlinear supersymmetry admits seven alternatives for a grading operator. One of its local, first order supercharges may be identified as a Hamiltonian of an associated one-gap, non-periodic Bogoliubov-de Gennes system. The latter possesses a nonlinear supersymmetric structure, in which any of the three non-local generators of a Clifford algebra may be chosen as the grading operator. We find that the supersymmetry generators for the both systems are the Darboux-dressed integrals of a free spin-1/2 particle in the Schrodinger picture, or of a free massive Dirac particle. Nonlocal Foldy- Wouthuysen transformations are shown to be involved in the supersymmetric structure.

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Mikhail S. Plyushchay, Luis-Miguel Nieto. 2010-09-26. Self-isospectrality, mirror symmetry, and exotic nonlinear supersymmetry. https://doi.org/10.1103/physrevd.82.065022

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