dorsal/arxiv
View SchemaNonlinear Pseudo-Supersymmetry in the Framework of N-fold Supersymmetry
| Authors | Artemio Gonzalez-Lopez, Toshiaki Tanaka |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0602177 |
| URL | https://arxiv.org/abs/quant-ph/0602177 |
| DOI | 10.1088/0305-4470/39/14/014 |
| Journal | J. Phys. A: Math. Gen. 39 (2006) 3715-3723 |
Abstract
We recall the importance of recognizing the different mathematical nature of various concepts relating to PT-symmetric quantum theories. After clarifying the relation between supersymmetry and pseudo-supersymmetry, we prove generically that nonlinear pseudo-supersymmetry, recently proposed by Sinha and Roy, is just a special case of N-fold supersymmetry. In particular, we show that all the models constructed by these authors have type A 2-fold supersymmetry. Furthermore, we prove that an arbitrary one-body quantum Hamiltonian which admits two (local) solutions in closed form belongs to type A 2-fold supersymmetry, irrespective of whether or not it is Hermitian, PT-symmetric, pseudo-Hermitian, and so on.
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"abstract": "We recall the importance of recognizing the different mathematical nature of\nvarious concepts relating to PT-symmetric quantum theories. After clarifying\nthe relation between supersymmetry and pseudo-supersymmetry, we prove\ngenerically that nonlinear pseudo-supersymmetry, recently proposed by Sinha and\nRoy, is just a special case of N-fold supersymmetry. In particular, we show\nthat all the models constructed by these authors have type A 2-fold\nsupersymmetry. Furthermore, we prove that an arbitrary one-body quantum\nHamiltonian which admits two (local) solutions in closed form belongs to type A\n2-fold supersymmetry, irrespective of whether or not it is Hermitian,\nPT-symmetric, pseudo-Hermitian, and so on.",
"arxiv_id": "quant-ph/0602177",
"authors": [
"Artemio Gonzalez-Lopez",
"Toshiaki Tanaka"
],
"categories": [
"quant-ph",
"math-ph",
"math.MP"
],
"doi": "10.1088/0305-4470/39/14/014",
"journal_ref": "J. Phys. A: Math. Gen. 39 (2006) 3715-3723",
"title": "Nonlinear Pseudo-Supersymmetry in the Framework of N-fold Supersymmetry",
"url": "https://arxiv.org/abs/quant-ph/0602177"
},
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