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OverviewThis book provides the most comprehensive mathematical treatment to date of the Feynman path integral and Feynman's operational calculus. It is accessible to mathematicians, mathematical physicists and theoretical physicists. Including new results and much material previously only available in the research literature, this book discusses both the mathematics and physics background that motivate the study of the Feynman path integral and Feynman's operational calculus, and also provides more detailed proofs of the central results. Full Product DetailsAuthor: Gerald W. Johnson (, Department of Mathematics and Statistics, University of Nebraska-Lincoln) , Michel L. Lapidus (, Department of Mathematics, University of California, Riverside)Publisher: Oxford University Press Imprint: Oxford University Press Dimensions: Width: 15.60cm , Height: 4.20cm , Length: 23.40cm Weight: 1.122kg ISBN: 9780198515722ISBN 10: 0198515723 Pages: 792 Publication Date: 17 January 2002 Audience: Professional and scholarly , Professional & Vocational Format: Paperback Publisher's Status: Active Availability: To order  Stock availability from the supplier is unknown. We will order it for you and ship this item to you once it is received by us. Table of Contents1: Introduction 2: The physical phenomenon of Brownian motion 3: Wiener measure 4: Scaling in Wiener space and the analytic Feynman integral 5: Stochastic processes and the Wiener process 6: Quantum dynamics and the Schroedinger equation 7: The Feynman integral: Heuristic ideas and mathematical difficulties 8: Semigroups of operators: An informal introduction 9: Linear semigroups of operators 10: Unbounded self-adjoint operators and quadratic forms 11: Product formulas with applications to the Feynman integral 12: The Feynman-Kac formula 13: Analytic-in-time or mass operator-valued Feynman integrals 14: Feynman's operational calculus for noncommuting operators: An introduction 15: Generalised Dyson series, the Feynman integral and Feynman's operational calculus 16: Stability results 17: The Feynman-Kac formula with a Lebesgue-Stieltjes measure and Feynman's operational calculus 18: Noncommutative operations on Wiener functionals, disentangling algebras and Feynman's operational calculus 19: Feynman's operational calculus and evolution equations 20: Further work on or related to the Feynman integral References Index of symbols Author index Subject indexReviews<br> 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<p><br> 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 not mathematically 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. It was clear to Feynman that his 'path integral' was no integral in the ordinary sense of the word, and that what he called its 'summation o 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 * 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. * Physics Today * 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. * EMS * <br> 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<p><br> 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 not mathematically 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. It was clear to Feynman that his 'path integral' was no integral in the ordinary sense of the word, and that what he called its 'summation over histories' did not involve a measure in the usual sense. ... The book by Johnson and Lapidus deals with various approaches to making the Feynman path integral into a mathematically meaningful object. ... I would recommend this book to serious students of the subject ... --Physics Today<p><br> <br> 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<br> 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 not mathematically 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. It was clear to Feynman that his 'path integral' was no integral in the ordinary sense of the word, and that what he called its 'summation over 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<br> 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 not mathematically 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. It was clear to Feynman that his 'path integral' was no integral in the ordinary sense of the word, and that what he called its 'summation over histories' did not involve a measure in the usual sense. ... The book by Johnson and Lapidus deals with various approaches to making the Feynman path integral into a mathematically meaningful object. ... I would recommend this book to serious students of the subject ... --Physics Today<br> Author InformationTab Content 6Author Website:Countries AvailableAll regions |
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