The Feynman Integral and Feynman’s Operational Calculus
The Feynman Integral and Feynman’s Operational Calculus by Gerald W. Johnson, published by Clarendon Press in 2000, is a comprehensive exploration of advanced mathematical concepts relevant to quantum theory. This reprint edition spans 771 pages and is presented in English. The book aims to make the intricate subjects of the Feynman integral and operational calculus accessible to mathematicians, physicists, and other scientists, detailing the existence and properties of these integrals under various conditions.
Readers will find a thorough examination of four distinct approaches to the Feynman integral, with a focus on their stability properties and agreement under specific conditions. The text includes background material in mathematics and physics that underpins the study of these topics, along with detailed proofs for the central results. This work also presents new findings and compiles material that was previously scattered in research literature, making it a valuable resource for those interested in the mathematical foundations of quantum dynamics.
Official synopsis Publisher
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.
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