**Graduate Studies in Mathematics**

Volume: 95;
2008;
387 pp;
Hardcover

MSC: Primary 81;

Print ISBN: 978-0-8218-4630-8

Product Code: GSM/95

List Price: $75.00

AMS Member Price: $60.00

MAA Member Price: $67.50

**Electronic ISBN: 978-1-4704-1162-6
Product Code: GSM/95.E**

List Price: $75.00

AMS Member Price: $60.00

MAA Member Price: $67.50

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#### Supplemental Materials

# Quantum Mechanics for Mathematicians

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*Leon A. Takhtajan*

This book provides a comprehensive treatment of quantum mechanics from a
mathematics perspective and is accessible to mathematicians starting with
second-year graduate students. In addition to traditional topics, like
classical mechanics, mathematical foundations of quantum mechanics,
quantization, and the Schrödinger equation, this book gives a mathematical
treatment of systems of identical particles with spin, and it introduces
the reader to functional methods in quantum mechanics. This includes the
Feynman path integral approach to quantum mechanics, integration in
functional spaces, the relation between Feynman and Wiener integrals,
Gaussian integration and regularized determinants of differential
operators, fermion systems and integration over anticommuting (Grassmann)
variables, supersymmetry and localization in loop spaces, and
supersymmetric derivation of the Atiyah-Singer formula for the index of
the Dirac operator. Prior to this book, mathematicians could find these
topics only in physics textbooks and in specialized literature.

This book is written in a concise style with careful attention to precise
mathematics formulation of methods and results. Numerous problems, from
routine to advanced, help the reader to master the subject. In addition to
providing a fundamental knowledge of quantum mechanics, this book could
also serve as a bridge for studying more advanced topics in quantum
physics, among them quantum field theory.

Prerequisites include standard first-year graduate courses covering linear
and abstract algebra, topology and geometry, and real and complex
analysis.

#### Readership

Graduate students and research mathematicians interested in mathematical aspects of quantum mechanics.

#### Reviews & Endorsements

...heaven-sent to the aforementioned analytic number theorist, i.e., me, because it is mathematics, not physics: the exposition is peppered with definitions and theorems, and proofs!, proofs!, proofs!...

-- Michael Berg for MAA Reviews

By a clever selection of the material and the clear way of exposing it, the book is recommended for graduate students in mathematics looking for applications in physics, as well as for student in physics desiring to be acquainted, in a rigorous but, at the same time, quick and accessible manner, with the basic mathematical tools used in quantum mathematics.

-- Studia Universitatis Babes-Bolyai, Mathematica

#### Table of Contents

# Table of Contents

## Quantum Mechanics for Mathematicians

- Cover Cover11 free
- Title page iii4 free
- Contents vii8 free
- Preface xiii14 free
- Part I. Foundations 118 free
- Classical mechanics 320
- Basic principles of quantum mechanics 6380
- Schrödinger equation 149166
- Spin and identical particles 217234
- Part II. Functional methods and supersymmetry 237254
- Path integral formulation of quantum mechanics 239256
- Integration in functional spaces 289306
- Fermion systems 307324
- Supersymmetry 343360
- Bibliography 373390
- Index 383400 free
- Back Cover Back Cover1410