Functional Integrals

Author : Barry Simon
Publisher : American Mathematical Soc.
ISBN 13 : 0821835823
Total Pages : 322 pages
Book Rating : 4.21/5 ( download)

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Download or read book Functional Integration and Quantum Physics written by Barry Simon and published by American Mathematical Soc.. This book was released on 2005 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : John R. Klauder
Publisher : Springer Science & Business Media
ISBN 13 : 0817647902
Total Pages : 292 pages
Book Rating : 4.02/5 ( download)

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Download or read book A Modern Approach to Functional Integration written by John R. Klauder and published by Springer Science & Business Media. This book was released on 2010-11-17 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : A.D. Egorov
Publisher : Springer Science & Business Media
ISBN 13 : 9401117616
Total Pages : 421 pages
Book Rating : 4.16/5 ( download)

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Download or read book Functional Integrals written by A.D. Egorov and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 421 pages. Available in PDF, EPUB and Kindle. Book excerpt: Integration in infinitely dimensional spaces (continual integration) is a powerful mathematical tool which is widely used in a number of fields of modern mathematics, such as analysis, the theory of differential and integral equations, probability theory and the theory of random processes. This monograph is devoted to numerical approximation methods of continual integration. A systematic description is given of the approximate computation methods of functional integrals on a wide class of measures, including measures generated by homogeneous random processes with independent increments and Gaussian processes. Many applications to problems which originate from analysis, probability and quantum physics are presented. This book will be of interest to mathematicians and physicists, including specialists in computational mathematics, functional and statistical physics, nuclear physics and quantum optics.

Author : V.N. Popov
Publisher : Springer Science & Business Media
ISBN 13 : 9781402003073
Total Pages : 316 pages
Book Rating : 4.72/5 ( download)

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Download or read book Functional Integrals in Quantum Field Theory and Statistical Physics written by V.N. Popov and published by Springer Science & Business Media. This book was released on 2001-11-30 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: Functional integration is one of the most powerful methods of contempo rary theoretical physics, enabling us to simplify, accelerate, and make clearer the process of the theoretician's analytical work. Interest in this method and the endeavour to master it creatively grows incessantly. This book presents a study of the application of functional integration methods to a wide range of contemporary theoretical physics problems. The concept of a functional integral is introduced as a method of quantizing finite-dimensional mechanical systems, as an alternative to ordinary quantum mechanics. The problems of systems quantization with constraints and the manifolds quantization are presented here for the first time in a monograph. The application of the functional integration methods to systems with an infinite number of degrees of freedom allows one to uniquely introduce and formulate the diagram perturbation theory in quantum field theory and statistical physics. This approach is significantly simpler than the widely accepted method using an operator approach.

Author : Cécile Dewitt-Morette
Publisher : Springer Science & Business Media
ISBN 13 : 1489903194
Total Pages : 436 pages
Book Rating : 4.98/5 ( download)

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Download or read book Functional Integration written by Cécile Dewitt-Morette and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 436 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Hagen Kleinert
Publisher : World Scientific
ISBN 13 : 9814273570
Total Pages : 1626 pages
Book Rating : 4.72/5 ( download)

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Download or read book Path Integrals in Quantum Mechanics, Statistics, Polymer Physics, and Financial Markets written by Hagen Kleinert and published by World Scientific. This book was released on 2009 with total page 1626 pages. Available in PDF, EPUB and Kindle. Book excerpt: Topological restrictions. These are relevant to the understanding of the statistical properties of elementary particles and the entanglement phenomena in polymer physics and biophysics. The Chern-Simons theory of particles with fractional statistics (anyons) is introduced and applied to explain the fractional quantum Hall effect." "The relevance of path integrals to financial markets is discussed, and improvements of the famous Black-Scholes formula for option prices are developed which account for the fact that large market fluctuations occur much more frequently than in Gaussian distributions." --Book Jacket.

Author : Mark Iosifovich Freidlin
Publisher : Princeton University Press
ISBN 13 : 1400881595
Total Pages : 560 pages
Book Rating : 4.98/5 ( download)

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Download or read book Functional Integration and Partial Differential Equations. (AM-109), Volume 109 written by Mark Iosifovich Freidlin and published by Princeton University Press. This book was released on 2016-03-02 with total page 560 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book discusses some aspects of the theory of partial differential equations from the viewpoint of probability theory. It is intended not only for specialists in partial differential equations or probability theory but also for specialists in asymptotic methods and in functional analysis. It is also of interest to physicists who use functional integrals in their research. The work contains results that have not previously appeared in book form, including research contributions of the author.

Author : L. S. Schulman
Publisher : Courier Corporation
ISBN 13 : 0486137023
Total Pages : 434 pages
Book Rating : 4.25/5 ( download)

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Download or read book Techniques and Applications of Path Integration written by L. S. Schulman and published by Courier Corporation. This book was released on 2012-10-10 with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt: Suitable for advanced undergraduates and graduate students, this text develops the techniques of path integration and deals with applications, covering a host of illustrative examples. 26 figures. 1981 edition.

Author : Wen-Wei Li
Publisher : Springer
ISBN 13 : 3030012883
Total Pages : 148 pages
Book Rating : 4.85/5 ( download)

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Download or read book Zeta Integrals, Schwartz Spaces and Local Functional Equations written by Wen-Wei Li and published by Springer. This book was released on 2018-11-02 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on a conjectural class of zeta integrals which arose from a program born in the work of Braverman and Kazhdan around the year 2000, the eventual goal being to prove the analytic continuation and functional equation of automorphic L-functions. Developing a general framework that could accommodate Schwartz spaces and the corresponding zeta integrals, the author establishes a formalism, states desiderata and conjectures, draws implications from these assumptions, and shows how known examples fit into this framework, supporting Sakellaridis' vision of the subject. The collected results, both old and new, and the included extensive bibliography, will be valuable to anyone who wishes to understand this program, and to those who are already working on it and want to overcome certain frequently occurring technical difficulties.

Author : Victor Nikolaevich Popov
Publisher : Cambridge University Press
ISBN 13 : 9780521307772
Total Pages : 224 pages
Book Rating : 4.75/5 ( download)

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Download or read book Functional Integrals and Collective Excitations written by Victor Nikolaevich Popov and published by Cambridge University Press. This book was released on 1987 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: A distinguished physicist and leading researcher describes the theory and selected applications of one of the most important mathematical tools used in the theoretical investigation of collective excitations in statistical physics.