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VOL. 22 | 1989 Supersymmetric quantum mechanics and the index theorem
P. D. Jarvis

Editor(s) Michael N. Barber, Michael K. Murray

Abstract

The basic features of supersymmetric quantum mechanics are reviewed and illustrated by examples from physics and geometry (the hydrogen atom, and massless fields in curved space). Using a discrete approximation to the path integral in the associated supersymmetric quantum mechanics, the Atiyah-Singer Index Theorem is derived for the twisted Diraf operator. Specializations of this in four dimensions include the Gauss-Bonnet theorem, and the Hirzebruch signature theorem. The relationship of the index theorem to anomalies, and their cancellation in the standard model and beyond, is briefly discussed.

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Published: 1 January 1989
First available in Project Euclid: 19 November 2014

zbMATH: 0702.58072
MathSciNet: MR1027861

Rights: Copyright © 1989, Centre for Mathematics and its Applications, Mathematical Sciences Institute, The Australian National University. This book is copyright. Apart from any fair dealing for the purpose of private study, research, criticism or review as permitted under the Copyright Act, no part may be reproduced by any process without permission. Inquiries should be made to the publisher.

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Vol. 22 • 1 January 1989
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