The Feynman Integral and Feynman's Operational Calculus (Oxford Mathematical Monographs) [Paperback]

Gerald W. Johnson (Author), Michel L. Lapidus (Author)

Book Description

ISBN-10: 0198515723 | ISBN-13: 978-0198515722 | Publication Date: March 28, 2002

The aim of this book is to make accessible to mathematicians, physicists and other scientists interested in quantum theory, the mathematically beautiful but difficult subjects of the Feynman integral and Feynman's operational calculus. Some advantages of the four approaches to the Feynman integral which are given detailed treatment 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 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.

Editorial Reviews

Review

"A most scholarly text which is comprehensive, detailed and very clearly written. It embraces the whole of the topic not just one part of it, and the historical references give an insight into the development of the ideas behind this fascinating approach to quantum theory. Written by experts who are also good teachers."--Aslib Book Guide

"The idea behind the Feynman path integral goes back to a paper by P. A. M. Dirac published in 1933 in Physikalische Zeitschrift der Sowjetunion. It formed the core of Richard Feynman's space-time approach to quantum mechanics and quantum electrodynamics. Although the path integral was not mathematically well defined, it was widely used in quantum field theory, statistical mechanics, and string theory. Recently, path integrals have been the heuristic guide to spectacular developments in pure mathematics. It was clear to Feynman that his 'path integral' was no integral in the ordinary sense of the word, and that what he called its 'summation over histories' did not involve a measure in the usual sense. ... The book by Johnson and Lapidus deals with various approaches to making the Feynman path integral into a mathematically meaningful object. ... I would recommend this book to serious students of the subject ..."--Physics Today

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.

Product Details

• Paperback: 792 pages
• Publisher: Oxford University Press, USA (March 28, 2002)
• Language: English
• ISBN-10: 0198515723
• ISBN-13: 978-0198515722
• Product Dimensions: 9.1 x 6.1 x 1.8 inches
• Shipping Weight: 2.6 pounds (View shipping rates and policies)
• Average Customer Review: 5.0 out of 5 stars  See all reviews (1 customer review)
• Amazon Best Sellers Rank: #2,470,091 in Books (See Top 100 in Books)

More About the Author

Discover books, learn about writers, read author blogs, and more.

Customer Reviews

Most Helpful Customer Reviews

11 of 12 people found the following review helpful:

5.0 out of 5 stars An Excellent Volume!, February 9, 2001

By 

Lance Nielsen (Omaha, NE USA) - See all my reviews

This review is from: The Feynman Integral and Feynman's Operational Calculus (Oxford Mathematical Monographs) (Hardcover)

This volume by Johnson and Lapidus is an excellent guide to the Feynman integral and Feynman's operational calculus. The authors bring together a great deal of the background material needed for the study of the integral and operational calculus so as to make the volume mostly self-contained.

The book contains several different approaches to the Feynman integral and discusses in some detail relationships between these approaches. The exposition is very clear and detailed and the proofs of results in the text are detailed and extremely well written. Also, the text contains many items that have only appeared in the research literature. Some of these results are quite new.

Also contained in this text is a thorough discussion of Feynman's operational calculus, again from more than one point of view. Many of the results contained here have only appeared previously in the research literature and again some are quite recent. This part of the book is also very well and clearly written.

There are also many remarks and examples dealing with the applicability of the formalism to physical situations.

This is a great read for anyone wanting to further there knowledge about these subjects.