Simultaneous Ordinary and Type A N-fold Supersymmetries in Schroedinger, Pauli, and Dirac Equations
arXiv:hep-th/0509020 · doi:10.1016/j.aop.2005.12.008
Abstract
We investigate physical models which possess simultaneous ordinary and type A N-fold supersymmetries, which we call type A (N,1)-fold supersymmetry. Inequivalent type A (N,1)-fold supersymmetric models with real-valued potentials are completely classified. Among them, we find that a trigonometric Rosen-Morse type and its elliptic version are of physical interest. We investigate various aspects of these models, namely, dynamical breaking and interrelation between ordinary and N-fold supersymmetries, shape invariance, quasi-solvability, and an associated algebra which is composed of one bosonic and four fermionic operators and dubbed type A (N,1)-fold superalgebra. As realistic physical applications, we demonstrate how these systems can be embedded into Pauli and Dirac equations in external electromagnetic fields.
arXiv comment27 pages, 1 figure; typos corrected, Refs. updated, to appear in Annals of Physics
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