On supersymmetric and topological quantum mechanical models

Abstract

We explain the details of two supersymmetric quantum mechanical models. Their simplicity make them solvable although they share the characteristics of more sophisticated models based on the gauge fixing of topological invariants. The first model is a supersymmetric quantum mechanical system defined on a punctured plane and leads to topological observables which we compute. The absences of a ground state and of a mass gap are special features of this system. The second model is the supersymmetric description of spin-one particles moving in D-dimensional space-time. We show that it is a topological model in a space with two more dimensions.