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

Creators: Bollé, D.; Gesztesy, F.; Grosse, H.; Schweiger, W.; Simon, B.

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.

Additional Information

© 1987 American Institute of Physics. Received 13 November 1986; accepted 11 February 1987. We gratefully acknowledge stimulating discussions with Professor R. Blankenbecler. F. G. is indebted to Professor K. Chadan for the warm hospitality extended to him at LPTHE-Orsay, and to E. Stone and D. Wales for hospitality at Caltech. D. B. is an Onderzoeksleider of the National Fonds voor Wetenschappelijk Onderzoek, Belgium. The work of F. G. and H. G. is partially supported by Fonds zur Förderung der Wissenschaftlichen Forschung in Österreich, Project No. P5588. The research of B. S. is partially supported by the USNSF under Grant No. DMS-84-16049.

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