Functional Integration
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Functional Integration And Quantum Physics
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Author : Barry Simon
language : en
Publisher: American Mathematical Soc.
Release Date : 2005
Functional Integration And Quantum Physics written by Barry Simon and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Integration, Functional categories.
Focuses on probabilistic foundations of the Feynman-Kac formula. Starting with main examples of Gaussian processes (the Brownian motion, the oscillatory process, and the Brownian bridge), this book presents four different proofs of the Feynman-Kac formula.
Functional Integration
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Author : Cécile Dewitt-Morette
language : en
Publisher: Springer
Release Date : 1997-09-30
Functional Integration written by Cécile Dewitt-Morette and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-09-30 with Mathematics categories.
The program of the Institute covered several aspects of functional integration -from a robust mathematical foundation to many applications, heuristic and rigorous, in mathematics, physics, and chemistry. It included analytic and numerical computational techniques. One of the goals was to encourage cross-fertilization between these various aspects and disciplines. The first week was focused on quantum and classical systems with a finite number of degrees of freedom; the second week on field theories. During the first week the basic course, given by P. Cartier, was a presentation of a recent rigorous approach to functional integration which does not resort to discretization, nor to analytic continuation. It provides a definition of functional integrals simpler and more powerful than the original ones. Could this approach accommodate the works presented by the other lecturers? Although much remains to be done before answering "Yes," there seems to be no major obstacle along the road. The other courses taught during the first week presented: a) a solid introduction to functional numerical techniques (A. Sokal) and their applications to functional integrals encountered in chemistry (N. Makri). b) integrals based on Poisson processes and their applications to wave propagation (S. K. Foong), in particular a wave-restorer or wave-designer algorithm yielding the initial wave profile when one can only observe its distortion through a dissipative medium. c) the formulation of a quantum equivalence principle (H. Kleinert) which. given the flat space theory, yields a well-defined quantum theory in spaces with curvature and torsion.
Functional Integration
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Author : Cécile Dewitt-Morette
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-11
Functional Integration written by Cécile Dewitt-Morette and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-11 with Science categories.
The program of the Institute covered several aspects of functional integration -from a robust mathematical foundation to many applications, heuristic and rigorous, in mathematics, physics, and chemistry. It included analytic and numerical computational techniques. One of the goals was to encourage cross-fertilization between these various aspects and disciplines. The first week was focused on quantum and classical systems with a finite number of degrees of freedom; the second week on field theories. During the first week the basic course, given by P. Cartier, was a presentation of a recent rigorous approach to functional integration which does not resort to discretization, nor to analytic continuation. It provides a definition of functional integrals simpler and more powerful than the original ones. Could this approach accommodate the works presented by the other lecturers? Although much remains to be done before answering "Yes," there seems to be no major obstacle along the road. The other courses taught during the first week presented: a) a solid introduction to functional numerical techniques (A. Sokal) and their applications to functional integrals encountered in chemistry (N. Makri). b) integrals based on Poisson processes and their applications to wave propagation (S. K. Foong), in particular a wave-restorer or wave-designer algorithm yielding the initial wave profile when one can only observe its distortion through a dissipative medium. c) the formulation of a quantum equivalence principle (H. Kleinert) which. given the flat space theory, yields a well-defined quantum theory in spaces with curvature and torsion.
Functional Integration
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Author : Jean-Pierre Antoine
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Functional Integration written by Jean-Pierre Antoine and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Computers categories.
The idea of the workshop on Functional Integration, Theory and Applications, held in Louvain-Ia-Neuve from November 6 to 9 1979, was to put in close and informal contact, during a few days, active workers in the field. There is no doubt now that functional integration is a tool that is being applied in all branches of modern physics. Since the earlier works of Dirac and Feynman enormous progress has been made, but unfortunately we lack still a unifying and rigo rous mathematical framework to account for all the situations in which one is interested. We are then in presence of a rapid ly changing field in which new achievements, proposals, and points of view are the normal pattern. Considering this state of affairs we have decided to order the articles starting from the more fundamental and ambitious from the point of view of mathematical rigour, followed by ar ticles in which the main interest is the application to con crete physical situations. It is obvious that this ordering should not be taken too seriously since in many cases there will be an interplay of both objects.
A Modern Approach To Functional Integration
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Author : John R. Klauder
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-11-17
A Modern Approach To Functional Integration written by John R. Klauder and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-11-17 with Mathematics categories.
This text takes advantage of recent developments in the theory of path integration and attempts to make a major paradigm shift in how the art of functional integration is practiced. The techniques developed in the work will prove valuable to graduate students and researchers in physics, chemistry, mathematical physics, and applied mathematics who find it necessary to deal with solutions to wave equations, both quantum and beyond. A Modern Approach to Functional Integration offers insight into a number of contemporary research topics, which may lead to improved methods and results that cannot be found elsewhere in the textbook literature. Exercises are included in most chapters, making the book suitable for a one-semester graduate course on functional integration.
Functional Integration
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Author :
language : en
Publisher:
Release Date : 1997
Functional Integration written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with categories.
Lectures On Quantum Field Theory And Functional Integration
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Author : Zbigniew Haba
language : en
Publisher: Springer Nature
Release Date : 2023-05-29
Lectures On Quantum Field Theory And Functional Integration written by Zbigniew Haba and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-05-29 with Science categories.
This book offers a concise introduction to quantum field theory and functional integration for students of physics and mathematics. Its aim is to explain mathematical methods developed in the 1970s and 1980s and apply these methods to standard models of quantum field theory. In contrast to other textbooks on quantum field theory, this book treats functional integration as a rigorous mathematical tool. More emphasis is placed on the mathematical framework as opposed to applications to particle physics. It is stressed that the functional integral approach, unlike the operator framework, is suitable for numerical simulations. The book arose from the author's teaching in Wroclaw and preserves the form of his lectures. So some topics are treated as an introduction to the problem rather than a complete solution with all details. Some of the mathematical methods described in the book resulted from the author's own research.
Functional Integration
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Author : Pierre Cartier
language : en
Publisher: Cambridge University Press
Release Date : 2006-11-30
Functional Integration written by Pierre Cartier and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-30 with Science categories.
In this text, Cartier and DeWitt-Morette, using their complementary interests and expertise, successfully condense and apply the essentials of Functional Integration to a great variety of systems, showing this mathematically elusive technique to be a robust, user friendly and multipurpose tool.
Functional Integration
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Author : Pierre Cartier
language : en
Publisher:
Release Date : 2006
Functional Integration written by Pierre Cartier and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Integration, Functional categories.
Functional integration successfully entered physics as path integrals in the 1942 Ph. D. dissertation of Richard P. Feynman, but it made no sense at all as a mathematical definition. Cartier and DeWitt-Morette have created, in this book, a fresh approach to functional integration. The book is self-contained: mathematical ideas are introduced, developed, generalised and applied. In the authors' hands, functional integration is shown to be a robust, user-friendly and multi-purpose tool that can be applied to a great variety of situations, for example: systems of indistinguishable particles; Aharonov-Bohm systems; supersymmetry; non-gaussian integrals. Problems in quantum field theory are also considered. In the final part the authors outline topics that can be profitably pursued using material already presented.
Functional Integration
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Author : Pierre Cartier
language : en
Publisher: Cambridge University Press
Release Date : 2010-06-10
Functional Integration written by Pierre Cartier and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-06-10 with Science categories.
Functional integration successfully entered physics as path integrals in the 1942 Ph.D. dissertation of Richard P. Feynman, but it made no sense at all as a mathematical definition. Cartier and DeWitt-Morette have created, in this book, a fresh approach to functional integration. The book is self-contained: mathematical ideas are introduced, developed, generalised and applied. In the authors' hands, functional integration is shown to be a robust, user-friendly and multi-purpose tool that can be applied to a great variety of situations, for example: systems of indistinguishable particles; Aharonov-Bohm systems; supersymmetry; non-gaussian integrals. Problems in quantum field theory are also considered. In the final part the authors outline topics that can be profitably pursued using material already presented.