Krein's spectral shift function and fredholm determinants as efficient methods to study supersymmetric quantum mechanics

Abstract

A new method is proposed to study supersymmetric quantum mechanics. A basic relation is derived between Krein's spectral shift function and the Witten index as a powerful tool for explicit model investigations. The topological invariance of relevant quantities like the index, the anomaly, the spectral asymmetry and the spectral shift function is proved. As an illustration, some model calculations are presented, in particular the two-dimensional magnetic field problem, without assuming the magnetic flux to be quantized.