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The idea of supersymmetry was originally introduced in relativistic
quantum field theories as a generalization of Poincare symmetry. In
1976 Nicolai sug gested an analogous generalization for
non-relativistic quantum mechanics. With the one-dimensional model
introduced by Witten in 1981, supersym metry became a major tool in
quantum mechanics and mathematical, sta tistical, and
condensed-IIll;l. tter physics. Supersymmetry is also a successful
concept in nuclear and atomic physics. An underlying supersymmetry
of a given quantum-mechanical system can be utilized to analyze the
properties of the system in an elegant and effective way. It is
even possible to obtain exact results thanks to supersymmetry. The
purpose of this book is to give an introduction to supersymmet ric
quantum mechanics and review some of the recent developments of
vari ous supersymmetric methods in quantum and statistical physics.
Thereby we will touch upon some topics related to mathematical and
condensed-matter physics. A discussion of supersymmetry in atomic
and nuclear physics is omit ted. However, the reader will find some
references in Chap. 9. Similarly, super symmetric field theories
and supergravity are not considered in this book. In fact, there
exist already many excellent textbooks and monographs on these
topics. A list may be found in Chap. 9. Yet, it is hoped that this
book may be useful in preparing a footing for a study of
supersymmetric theories in atomic, nuclear, and particle physics.
The plan of the book is as follows."
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