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

Bollé, D. and Gesztesy, F. and Grosse, H. and Schweiger, W. and Simon, B. (1987) Witten index, axial anomaly, and Krein's spectral shift function in supersymmetric quantum mechanics. Journal of Mathematical Physics, 28 (7). pp. 1512-1525. ISSN 0022-2488. http://resolver.caltech.edu/CaltechAUTHORS:20120622-081911618

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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.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1063/1.527508 DOIUNSPECIFIED
http://jmp.aip.org/resource/1/jmapaq/v28/i7/p1512_s1PublisherUNSPECIFIED
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.
Funders:
Funding AgencyGrant Number
Fonds Zur Förderung der Wissenschaftlichen ForschungP5588
NSFDMS-84-16049
Subject Keywords:QUANTUM MECHANICS, SUPERSYMMETRY, SCATTERING, INVARIANCE PRINCIPLES, SPECTRAL FUNCTIONS, SPECTRAL SHIFT, MAGNETIC FIELDS, MAGNETIC FLUX, QUANTUM FIELD THEORY, QUANTUM NUMBERS, QUANTUM OPERATORS, HAMILTONIANS, TOPOLOGY, FUNCTIONAL ANALYSIS
Classification Code:PACS: 03.65.Db, 11.30.Pb, 11.10.Ef
Record Number:CaltechAUTHORS:20120622-081911618
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20120622-081911618
Official Citation:Witten index, axial anomaly, and Krein’s spectral shift function in supersymmetric quantum mechanics D. Bollé, F. Gesztesy, H. Grosse, W. Schweiger, and B. Simon J. Math. Phys. 28, 1512 (1987); http://dx.doi.org/10.1063/1.527508
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:32024
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:22 Jun 2012 15:38
Last Modified:26 Dec 2012 15:22

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