Feynman Integral and Feynman's Operational Calculus

The aim of this book is to make accesible 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 Feynamn integrals agree with one another and with the unitary group from the usual approach to quantum dynamics; these same three Feynman integrals possess stability properties. Much of the material covered here was previously available only in the research literature, and the book also contains some recent 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.

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., 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., 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.