Supersymmetry and Models for Two Kinds of Interacting Particles

Abstract

We show that Calogero-Sutherland models for interacting particles have a natural supersymmetric extension. For the construction, we use Jacobians which appear in certain superspaces. Some of the resulting Hamiltonians have a direct physics interpretation as models for two kinds of interacting particles. One model may serve to describe interacting electrons in a lower and upper band of a quasi-one-dimensional semiconductor, another model corresponds to two kinds of particles confined to two different spatial directions with an interaction involving tensor forces.