The Feynman Integral and Feynman's Operational Calculus (Oxford Mathematical Monographs) - Hardcover

Johnson, Gerald W.

Hardcover

ISBN 10: 0198535740 ISBN 13: 9780198535744

Publisher: Oxford University Press, 2000

Synopsis

This text aims to make accessible to mathematicians, physicists and other scientists interested in quantum 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 has been 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.

About this title

Review

Review from previous edition: Accessible, even for beginners ... this book should serve as a standard reference for anybody interested in the mathematical theory of Feynman path integrals and the related operational calculus. (EMS)

Review from previous edition: The last chapter deals with other work related to the book's topics, ranging from alternative approaches to the path integral (so-called Fresnel integrals) to a very readable survey of the influence of Feynman integrals on contempary mathematics and physics. In particular, the authors discuss low dimensional topology and Edward Witten's approach to knot invariants, and they end with a discussion of Maxim Kontsevich's work on deformation quantization. I would recommend this book to serious students of the subject. (Physics Today)

The second one [part of the final chapter] is a most welcome presentation of recent extensions and applications of Feynman's approach to a whole range of physical models of major interest ... it is here that the power of Feynman's approach of inspiring both mathematicans and physicists is best evidentiated. (Zentrablatt Mathematik)

About the Author

Gerald W. Johnson is in the Department of Mathematics and Statistics, University of Nebraska-Lincoln. Michel L. Lapidus is in the Department of Mathematics, University of California, Riverside.

Edition details

• Publisher: Oxford University Press
• Publication date: 2000
• ISBN 10: 0198535740
• ISBN 13: 9780198535744
• Binding: Hardcover
• Language: English
• Number of pages: 256