The Feynman Integral and Feynman's Operational Calculus

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.'EMSReview 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 adiscussion 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

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.