The Feynman Integral and Feynman's Operational Calculus
Series: Oxford Mathematical Monographs;
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Product details:
- Publisher OUP Oxford
- Date of Publication 17 January 2002
- ISBN 9780198515722
- Binding Paperback
- No. of pages792 pages
- Size 234x156x42 mm
- Weight 1122 g
- Language English
- Illustrations numerous mathematical examples 0
Categories
Short description:
This book provides the most comprehensive mathematical treatment to date of the Feynman path integral. It is written so as to be accessible to mathematicians, mathematical physicists and theoretical physicists. A significant amount of background material is provided for the main topics, and complete proofs are given for most of the central results, making the book suitable for use in an advanced graduate course.
MoreLong description:
The aim of this book is to make accessible to mathematicians, physicists and other scientists interested in qunatum theory, the beautiful but mathematically difficult subjects of the Feynman integral and Feynman's operational calculus. Some advantages of the approaches to the Feynman integral which are treated in detail in this book are the following: the existence of the Feynman integral is established for very general potentials in all four cases; under more restrictive but still broad conditions, three of these Feynman integrals agree with one another and with the unitary group from the usual approach to quantum dynamics; these same three Feynman integrals possess pleasant stability properties. Much of the material covered here was previously available only in the research literature, and the book also contains some new results. The background material in mathematics and physics that motivates the study of the Feynman integral and Feynman's operational calculus is discussed, and detailed proofs are provided for the central results.
" I would recommend this book to serious students of the subject." Physics Today
Table of Contents:
Contents List - Page 1
1. Introduction
2. The physical phenomenon of Brownian motion
3. Wiener measure
4. Scaling in Wiener space and the analytic Feynman integral
5. Stochastic processes and the Wiener process
6. Quantum dynamics and the Schroedinger equation
7. The Feynman integral: Heuristic ideas and mathematical difficulties
8. Semigroups of operators: An informal introduction
9. Linear semigroups of operators
10. Unbounded self-adjoint operators and quadratic forms
11. Product formulas with applications to the Feynman integral
12. The Feynman-Kac formula
13. Analytic-in-time or mass operator-valued Feynman integrals
14. Feynman's operational calculus for noncommuting operators: An introduction
15. Generalised Dyson series, the Feynman integral and Feynman's operational calculus
16. Stability results
17. The Feynman-Kac formula with a Lebesgue-Stieltjes measure and Feynman's operational calculus
18. Noncommutative operations on Wiener functionals, disentangling algebras and Feynman's operational calculus
19. Feynman's operational calculus and evolution equations
20. Further work on or related to the Feynman integral
References
Index of symbols
Author index
Subject index
