Feynman Integral And Feynman'S Operational Calculu

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. "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 It embraces the whole of the topic not just one part of it, and the historical references give an insight into the development of the ideas behind this fascinating approach to quantum theory.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 notmathematically 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.