Simultaneous Ordinary and Type A N-fold Supersymmetries in Schroedinger, Pauli, and Dirac Equations

TL;DR

This paper classifies models with simultaneous ordinary and type A N-fold supersymmetries, exploring their properties, algebraic structures, and physical applications in Pauli and Dirac equations under electromagnetic fields.

Contribution

It provides a complete classification of inequivalent type A (N,1)-fold supersymmetric models with real potentials and demonstrates their embedding into fundamental quantum equations.

Findings

Identified trigonometric and elliptic Rosen-Morse potentials as physically relevant models.

Analyzed dynamical breaking and interrelation of supersymmetries.

Constructed a novel superalgebra combining bosonic and fermionic operators.

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.