Existence of Different Intermediate Hamiltonians in Type A N-fold Supersymmetry II. The N=3 Case
arXiv:1002.1766 · doi:10.1016/j.aop.2010.02.018
Abstract
We continue the previous study on the existence of different intermediate Hamiltonians in type A N-fold supersymmetric systems and carry out an exhaustive investigation on the N=3 case. In contrast with the N=2 case, we find various patterns in the existence of intermediate Hamiltonians due to the presence of two different intermediate positions in a factorized type A 3-fold supercharge. In addition, all the N=3 models are strictly restricted to at most elliptic type, which enables us to make the complete classification of the systems which admit intermediate Hamiltonians. Finally, we show realizations of third-order parasupersymmetry and variant generalized 3-fold superalgebras by such systems.
32 pages, no figures