Witten index, axial anomaly, and Krein’s spectral shift function in supersymmetric quantum mechanics

Abstract

A new method is presented to study supersymmetric quantum mechanics. Using relative scattering techniques, basic relations are derived between Krein’s spectral shift function, the Witten index, and the anomaly. The topological invariance of the spectral shift function is discussed. The power of this method is illustrated by treating various models and calculating explicitly the spectral shift function, the Witten index, and the anomaly. In particular, a complete treatment of the two-dimensional magnetic field problem is given, without assuming that the magnetic flux is quantized.