Functional Integration and Quantum Physics, Second Edition (Hardback)

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.

Product Details

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

1. Introduction
2. Construction of Gaussian Processes
3. Some Fundamental Tools of Probability Theory

Part II. The Basic Processes

4. The Wiener Process, the Oscillator Process, and the Brownian Bridge
5. Regularity Properties—1
6. The Feynman-Kac Formula
7. Regularity and Recurrence Properties—2

Part III. Bound State Problems

8. The Birman-Schwinger Kernel and Lieb's Formula
9. Phase Space Bounds
10. The Classical Limit
11. Recurrence and Weak Coupling

Part IV. Inequalities

12. Correlation Inequalities
13. Other Inequalities: Log Concavity, Symmetric Rearrangement, Conditioning, Hypercontractivity

PART V. Magnetic Fields and Stochastic Integrals

14. Itô's Integral
15. Schrödinger Operators with Magnetic Fields
16. Introduction to Stochastic Calculus

PART VI. Asymptotics

17. Donsker's Theorem
18. Laplace's Method in Function Space
19. Introduction to the Donsker-Varadhan Theory

PART VII. Other Topics

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

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