Self-isospectrality, mirror symmetry, and exotic nonlinear supersymmetry

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.

arXiv comment20 pages, comment added. Published version

References in corpus (37)

• Hidden Symmetries of the AdS_5 x S^5 Superstring
• Supersymmetric Yang-Mills Systems And Integrable Systems
• Structure of Resonance in Preheating after Inflation
• Classical/quantum integrability in AdS/CFT
• Higher-Derivative Supersymmetry and the Witten Index
• The all loop AdS4/CFT3 Bethe ansatz
• Inhomogeneous Condensates in the Thermodynamics of the Chiral NJL_2 model
• Deformed Heisenberg algebra, fractional spin fields and supersymmetry without fermions
• Self-consistent crystalline condensate in chiral Gross-Neveu and Bogoliubov-de Gennes systems
• On Integrability of Classical SuperStrings in AdS_5 x S^5
• Self-isospectrality, special supersymmetry, and their effect on the band structure
• Self-Isospectral Periodic Potentials and Supersymmetric Quantum Mechanics
• Hidden supersymmetry in quantum bosonic systems
• Nonlinear supersymmetry in Quantum Mechanics: algebraic properties and differential representation
• On the Dynamics of Finite-Gap Solutions in Classical String Theory
• Full Phase Diagram of the Massive Gross-Neveu Model
• Nonlinear Supersymmetry, Quantum Anomaly and Quasi-Exactly Solvable Systems
• SUSUSY quantum mechanics
• All about the Static Fermion Bags in the Gross-Neveu Model
• Aharonov-Bohm effect on AdS_2 and nonlinear supersymmetry of reflectionless Poschl-Teller system
• Field theory models for tachyon and gauge field string dynamics
• A Solvable Toy Model for Tachyon Condensation in String Field Theory
• Resonance Structure for Preheating with Massless Fields
• The Bogoliubov/de Gennes system, the AKNS hierarchy, and nonlinear quantum mechanical supersymmetry
• Hidden nonlinear supersymmetries in pure parabosonic systems
• Finite-gap systems, tri-supersymmetry and self-isospectrality
• The Ruijsenaars-Schneider Model in the Context of Seiberg-Witten Theory
• Hidden nonlinear supersymmetry of finite-gap Lame equation
• Three aspects of bosonized supersymmetry and linear differential field equation with reflection
• The Phenomenon of Darboux Displacements
• The origin of the hidden supersymmetry
• On Kinks and Bound States in the Gross-Neveu Model
• A BPS Interpretation of Shape Invariance
• The Lame equation in parametric resonance after inflation
• Exactly solvable associated Lame potentials and supersymmetric transformations
• Peculiarities of the hidden nonlinear supersymmetry of Poschl-Teller system in the light of Lame equation
• Generalized Supersymmetric Quantum Mechanics and Reflectionless Fermion Bags in 1+1 Dimensions

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