N-fold Supersymmetry for a Periodic Potential

Abstract

We report a new type of supersymmetry, "N-fold supersymmetry", in one-dimensional quantum mechanics. Its supercharges are N-th order polynomials of momentum: It reduces to ordinary supersymmetry for N=1, but for other values of N the anticommutator of the supercharges is not the ordinary Hamiltonian, but is a polynomial of the Hamiltonian. (For this reason, the original Hamiltonian is referred to as the "Mother Hamiltonian".) This supersymmetry shares some features with the ordinary variety, the most notable of which is the non-renormalization theorem. An N-fold supersymmetry was earlier found for a quartic potential whose supersymmetry is spontaneously broken. Here we report that it also holds for a periodic potential, albeit with somewhat different supercharges, whose supersymmetry is not broken.

10 pages, 2 figures

Cited by in corpus (21)

• N-fold Supersymmetry in Quantum Mechanics - General Formalism -
• Nonlinear supersymmetry in Quantum Mechanics: algebraic properties and differential representation
• General Forms of a N-fold Supersymmetric Family
• Nonlinear Supersymmetry, Quantum Anomaly and Quasi-Exactly Solvable Systems
• Quantum Inozemtsev model, quasi-exact solvability and N-fold supersymmetry
• Nonlocal supersymmetric deformations of periodic potentials
• Non-linear Supersymmetry for non-Hermitian, non-diagonalizable Hamiltonians: I. General properties
• Nonlinear supersymmetry on the plane in magnetic field and quasi-exactly solvable systems
• The Quantum Mechanics SUSY Algebra: An Introductory Review
• On hidden broken nonlinear superconformal symmetry of conformal mechanics and nature of double nonlinear superconformal symmetry
• A New Family of N-fold Supersymmetry: Type B
• Type A N-fold Supersymmetry and Generalized Bender-Dunne Polynomials
• sl(2) Construction of Type A N-fold supersymmetry
• N-fold Supersymmetry in Quantum Mechanics - Analyses of Particular Models -
• Classification of Type A N-fold supersymmetry
• sl(M+1) Construction of Quasi-solvable Quantum M-body Systems
• $\mathcal{P}\mathcal{T}$ symmetric models with nonlinear pseudo supersymmetry
• Hierarchy of QM SUSYs on a Bounded Domain
• Reducibility and bosonization of parasupersymmetric and orthosupersymmetric quantum mechanics
• A Family of Quasi-solvable Quantum Many-body Systems
• Higher order intertwining approach to quasinormal modes