Publication: Nonlinear pseudo-supersymmetry in the framework of N-fold supersymmetry
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2006-04-07
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IOP Publishing
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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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This work was partially supported by Spain’s DGI under the grant No. BFM2002-02646 (AG-L) as well as by the National Science Council of the Republic of China under the grant No. NSC-93-2112-M-032-009 (TT).
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