**AMS Chelsea Publishing**

Volume: 351;
2005;
306 pp;
Hardcover

MSC: Primary 81;
Secondary 58; 60

Print ISBN: 978-0-8218-3582-1

Product Code: CHEL/351.H

List Price: $46.00

AMS Member Price: $41.40

MAA Member Price: $41.40

**Electronic ISBN: 978-1-4704-3027-6
Product Code: CHEL/351.H.E**

List Price: $46.00

AMS Member Price: $41.40

MAA Member Price: $41.40

#### Supplemental Materials

# Functional Integration and Quantum Physics: Second Edition

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*Barry Simon*

AMS Chelsea Publishing: An Imprint of the American Mathematical Society

The main theme of this book is the “path integral
technique” and its applications to constructive methods of
quantum physics. The central topic is probabilistic foundations of the
Feynman–Kac formula. Starting with the main examples of Gaussian
processes (the Brownian motion, the oscillatory process, and the Brownian
bridge), the author presents four different proofs of the
Feynman–Kac formula. Also included is a simple exposition of
stochastic Itô calculus and its applications, in particular to
the Hamiltonian of a particle in a magnetic field (the
Feynman–Kac–Itô formula).

Among other topics discussed are the probabilistic approach to the bound
of the number of ground states of correlation inequalities (the
Birman–Schwinger principle, Lieb's formula, etc.), the calculation of
asymptotics for functional integrals of Laplace type (the theory of
Donsker–Varadhan) and applications, scattering theory, the theory of
crushed ice, and the Wiener sausage.

Written with great care and containing many highly illuminating examples,
this classic book is highly recommended to anyone interested in
applications of functional integration to quantum physics. It can also
serve as a textbook for a course in functional integration.

#### Readership

Graduate students and research mathematicians interested in probability and applications of functional integration to quantum physics.

#### Table of Contents

# Table of Contents

## Functional Integration and Quantum Physics: Second Edition

- Cover Cover11
- Title page iii4
- Contents v6
- Preface to the second edition vii8
- Preface ix10
- List of symbols xi12
- Functional integration and quantum physics xiii14
- Introduction 116
- The basic processes 3247
- Bound state problems 88103
- Inequalities 119134
- Magnetic fields and stochastic integrals 148163
- Asymptotics 174189
- Other topics 211226
- References 279294
- Index 293308
- Bibliographic supplement 297312
- Bibliography 301316
- Back Cover Back Cover1322