The Feynman Integral and Feynman’s Operational Calculus

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 Feynmanintegral 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 theunitary 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 mathematicsand 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.

Suitable for mathematicians, mathematical physicists and theoretical physicists, this book discusses both the mathematics and physics background that motivate the study of the Feynman path integral and Feynman's operational calculus. It also provides detailed proofs of the central results.

1: Introduction