Nonlinear Pseudo-Supersymmetry in the Framework of N-fold Supersymmetry

Details Nonlinear Pseudo-Supersymmetry in the Framework of N-fold Supersymmetry Nonlinear Pseudo-Supersymmetry in the Framework of N-fold Supersymmetry

2006-02-22

arxiv.org/abs/quant-ph/0602177v2

J. Phys. A: Math. Gen. 39 (2006) 3715-3723

Physics

Quantum Physics

10 pages, no figures; typos corrected

Scientific paper

10.1088/0305-4470/39/14/014

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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