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.
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