HIGHER-DERIVATIVE SUPERSYMMETRY AND THE WITTEN INDEX

We propose a higher-order derivative generation of supersymmetric quantum mechanics. It is formally based on the standard superalgebra but supercharges involve differential operators of order n. As a result, their anticommutator entails a polynomial of a Hamiltonian. The Witten index does not characterize spontaneous SUSY breaking in such models. The construction naturally arises after truncation of the order n parasupersymmetric quantum mechanics which in turn is built by glueing of n ordinary supersymmetric systems.