Supersymmetric quantum mechanics defined as sesquilinear forms

Abstract

A formulation of supersymmetric quantum mechanics in terms of sesquilinear forms is presented. Otherwise occurring rather complicated domain questions are solved in a simple and natural way. The authors formulate the axioms and describe a number of models. Supersymmetry transformations are implemented as superunitary transformations in a space defined over a Grassmann algebra, generalised Bogoliubov transformations acting in that space are also formulated.