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

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.

10 pages, no figures; typos corrected

References in corpus (3)

• MHD alpha^2-dynamo, Squire equation and PT-symmetric interpolation between square well and harmonic oscillator
• N-fold Supersymmetry in Quantum Systems with Position-dependent Mass
• A Novel Multi-parameter Family of Quantum Systems with Partially Broken N-fold Supersymmetry

Cited by in corpus (9)

• Making Sense of Non-Hermitian Hamiltonians
• Shape-invariant quantum Hamiltonian with position-dependent effective mass through second order supersymmetry
• Krein-Space Formulation of PT-Symmetry, CPT-Inner Products, and Pseudo-Hermiticity
• PT-Symmetric Quantum Theory Defined in a Krein Space
• General Aspects of PT-Symmetric and P-Self-Adjoint Quantum Theory in a Krein Space
• Irreducible second order SUSY transformations between real and complex potentials
• Existence of Different Intermediate Hamiltonians in Type A N-fold Supersymmetry
• Quasi-Hermitian supersymmetric extensions of a non-Hermitian oscillator Hamiltonian and of its generalizations
• On Existence of a Biorthonormal Basis Composed of Eigenvectors of Non-Hermitian Operators