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Self-isospectrality, mirror symmetry, and exotic nonlinear supersymmetry
High Energy Physics - Theory · Submitted 12 Jul 2010
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim 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.
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The abstract, sentence by sentence
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.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | 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. | contribution 0.97 | 0.89 | 0.09 | asserted 0.95 |
| s1 | The revealed exotic, partially broken nonlinear supersymmetry admits seven alternatives for a grading operator. | result 1.00 | 0.87 | 0.29 | asserted 0.99 |
| s2 | One of its local, first order supercharges may be identified as a Hamiltonian of an associated one-gap, non-periodic Bogoliubov-de Gennes system. | result 0.99 | 0.82 | 0.15 | hedged possibility 0.99 |
| s3 | 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. | result 0.98 | 0.70 | 0.15 | asserted 0.78 |
| s4 | 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. | result 0.99 | 0.93 | 0.27 | asserted 1.00 |
| s5 | Nonlocal Foldy- Wouthuysen transformations are shown to be involved in the supersymmetric structure. | result 0.89 | 0.80 | 0.10 | asserted 1.00 |
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The paper
Original 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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References
How the literature uses it
14 arXiv papers cite this in 27 sentences
Papers citing it · 24 sentences without a confident label
Compares with it 1 paper
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Particularly, the treatment of $𝒫_n;a$ as odd supercharges is possible, see [ref] .
Effect of scalings and translations on the supersymmetric quantum mechanical structure of soliton systems · Discussion and outlook · 0.87
Cites it as background 2 papers
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There may exist, at least at zero isospin chemical potential, other more preferable spatially non-uniform ground state configurations of the chiral condensate like, for instance, chiral crystals [ref] ) (in the last case only the scalar $q̅q$ condensate is an inhomogeneous quantity, and other condensates are homogeneous ones), but, in general, they are much harder to deal with.
Chiral density waves in the NJL$_2$ model with quark number and isospin chemical potentials · Introduction · 0.92
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The alternative choices for $Γ$ find some interesting physical applications, see [ref] , and we return to the discussion of this point in the last Section.
Effect of scalings and translations on the supersymmetric quantum mechanical structure of soliton systems · Supersymmetry of $n=1$ reflectionless pair with distinct scalings · 0.81
What it cites · 16 sentences without a confident label
Cites as background 18 papers
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Braden and Macfarlane [ref] , and in a more broad context Dunne and Feinberg [ref] revealed that a linear N = 2 supersymmetric extension of the periodic finite-gap quantum systems may produce completely isospectral systems characterized by the same, but a shifted potential.
Self-Isospectral Periodic Potentials and Supersymmetric Quantum Mechanics · Introduction · 0.88
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A higher order generalization of the Darboux transformations, known as the Darboux-Crum transformations [ref] , gives rise to a higher derivative generalization of supersymmetric quantum mechanics [ref] , characterized by nonlinear superalgebraic relations [ref] .
SUSUSY quantum mechanics · Introduction · 0.87
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A higher order generalization of the Darboux transformations, known as the Darboux-Crum transformations [ref] , gives rise to a higher derivative generalization of supersymmetric quantum mechanics [ref] , characterized by nonlinear superalgebraic relations [ref] .
Nonlinear Supersymmetry, Quantum Anomaly and Quasi-Exactly Solvable Systems · Introduction · 0.87
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