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## Functional Integration and Quantum Physics, Second Edition (Hardback)"Ever since the first edition went out of print, I have been approached by people asking how to get a copy. So, I'm glad that the AMS agreed to do this reprinting in the Chelsea series. The material has worn well, and if I were writing about this today, I wouldn't change much. There have been many developments over the past thirty years—after the index, I've added a brief bibliographic note on some of these developments." — Barry Simon, Author, in the Preface to the Second Edition (page vii) ## $23.95 |

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Please contact us if you've got questions about this product.## Condition

**VERY GOOD:** This book’s cover carries the most signs of use and wear, but only slightly. The remainder of the book is in excellent, like-new condition. The book was printed on acid-free paper.

## Description

Synopsis by Bowker: “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 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 Ito calculus and its applications, in particular to the Hamiltonian of a particle in a magnetic field (the Feynman-Kac-Ito 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.”

**BRIEF CONTENTS**

The book begins with Preface to the Second Edition, Preface, and List of Symbols.

**Part I. Introduction**

- Introduction
- Construction of Gaussian Processes
- Some Fundamental Tools of Probability Theory

**Part II. The Basic Processes**

- The Wiener Process, the Oscillator Process, and the Brownian Bridge
- Regularity Properties—1
- The Feynman-Kac Formula
- Regularity and Recurrence Properties—2

**Part III. Bound State Problems**

- The Birman-Schwinger Kernel and Lieb’s Formula
- Phase Space Bounds
- The Classical Limit
- Recurrence and Weak Coupling

**Part IV. Inequalities**

- Correlation Inequalities
- Other Inequalities: Log Concavity, Symmetric Rearrangement, Conditioning, Hypercontractivity

**PART V. Magnetic Fields and Stochastic Integrals**

- Itô’s Integral
- Schrödinger Operators with Magnetic Fields
- Introduction to Stochastic Calculus

**PART VI. Asymptotics**

- Donsker’s Theorem
- Laplace’s Method in Function Space
- Introduction to the Donsker-Varadhan Theory

**PART VII. Other Topics**

- Perturbation Theory for the Ground State Energy
- Dirichlet Boundaries and Decoupling Singularities in Scattering Theory
- Crushed Ice and the Wiener Sausage
- The Statistical Mechanics of Charged Particles with Positive Definite Interactions
- An Introduction to Euclidean Quantum Field Theory
- Properties of Eigenfunctions, Wave Packets, and Green’s Functions
- Inverse Problems and the Feynman-Kac Forumula

The book ends with References, Index, Bibliographic Supplement, and Bibliography.

## Details

- SKU:
- 2258
- Author:
- Simon, Barry
- Publisher:
- AMS Chelsea Publishing
- Publish Date:
- 2005
- Format:
- Hardback
- Weight (pounds):
- 1.59
- Dimensions (W”xL”xH”):
- 7.2″x10.25″x0.9″
- ISBN-13:
- 9780821835821
- ISBN-10:
- 0821835823

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