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Author: Barry Simon
Publisher: American Mathematical Soc.
ISBN: 0821835823
Category : Mathematics
Languages : en
Pages : 322
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Book Description
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: Barry Simon
Publisher: American Mathematical Soc.
ISBN: 0821835823
Category : Mathematics
Languages : en
Pages : 322
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Book Description
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: 0817647910
Category : Mathematics
Languages : en
Pages : 292
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Book Description
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: Cécile Dewitt-Morette
Publisher: Springer Science & Business Media
ISBN: 1489903194
Category : Science
Languages : en
Pages : 436
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Book Description
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: Pierre Cartier
Publisher: Cambridge University Press
ISBN: 1139462881
Category : Science
Languages : en
Pages : 7
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Book Description
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.
Author: Jean-Pierre Antoine
Publisher: Springer Science & Business Media
ISBN: 1461570352
Category : Computers
Languages : en
Pages : 354
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Book Description
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.
Author: V.N. Popov
Publisher: Springer Science & Business Media
ISBN: 9781402003073
Category : Science
Languages : en
Pages : 316
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Book Description
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: Barry Wacksman
Publisher: John Wiley & Sons
ISBN: 1118907213
Category : Business & Economics
Languages : en
Pages : 261
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Book Description
In a world of fierce global competition and rapid technological change, traditional strategies for gaining market share and achieving efficiencies no longer yield the returns they once did. How can companies drive consumer preference and secure sustainable growth in this digital, social, and mobile age? The answer is through functional integration. Some of the world's most highly valued companies—including Amazon, Apple and Google—have harnessed this new business model to build highly interactive ecosystems of interrelated products and digital services, gaining new levels of customer engagement. Functional integration offers forward-looking brands a unique competitive edge by using transformative digital technologies to deliver high-value customer experiences, generate repeat business, and unlock lucrative new business-to-business revenue streams. Connected By Design is the first book to show business leaders and marketers exactly how to use functional integration to achieve transformative growth within any type of company. Based on R/GA's pioneering work with firms at the forefront of functional integration, Barry Wacksman and Chris Stutzman identify seven principles companies must follow in order to create and deliver new value for customers and capture new revenues. Connected By Design explains how functional integration drove the transformation of market-leading companies as diverse as Nike, General Motors, McCormick & Co., and Activision to establish authentic brand relationships with their customers, enter new categories, and develop new sources of income. With Connected by Design, any company can leverage technological disruption to redefine its mission and foster greater brand loyalty and engagement.
Author: Alexander A. Demkov
Publisher: Springer Science & Business Media
ISBN: 146149320X
Category : Technology & Engineering
Languages : en
Pages : 284
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Book Description
This book describes the basic physical principles of the oxide/semiconductor epitaxy and offers a view of the current state of the field. It shows how this technology enables large-scale integration of oxide electronic and photonic devices and describes possible hybrid semiconductor/oxide systems. The book incorporates both theoretical and experimental advances to explore the heteroepitaxy of tuned functional oxides and semiconductors to identify material, device and characterization challenges and to present the incredible potential in the realization of multifunctional devices and monolithic integration of materials and devices. Intended for a multidisciplined audience, Integration of Functional Oxides with Semiconductors describes processing techniques that enable atomic-level control of stoichiometry and structure and reviews characterization techniques for films, interfaces and device performance parameters. Fundamental challenges involved in joining covalent and ionic systems, chemical interactions at interfaces, multi-element materials that are sensitive to atomic-level compositional and structural changes are discussed in the context of the latest literature. Magnetic, ferroelectric and piezoelectric materials and the coupling between them will also be discussed. GaN, SiC, Si, GaAs and Ge semiconductors are covered within the context of optimizing next-generation device performance for monolithic device processing.
Author: Hagen Kleinert
Publisher: World Scientific
ISBN: 9814273570
Category : Business & Economics
Languages : en
Pages : 1626
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Book Description
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: Nick Laskin
Publisher: World Scientific
ISBN: 9813223812
Category : Science
Languages : en
Pages : 358
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Book Description
Fractional quantum mechanics is a recently emerged and rapidly developing field of quantum physics.This is the first monograph on fundamentals and physical applications of fractional quantum mechanics, written by its founder.The fractional Schrödinger equation and the fractional path integral are new fundamental physical concepts introduced and elaborated in the book. The fractional Schrödinger equation is a manifestation of fractional quantum mechanics. The fractional path integral is a new mathematical tool based on integration over Lévy flights. The fractional path integral method enhances the well-known Feynman path integral framework.Related topics covered in the text include time fractional quantum mechanics, fractional statistical mechanics, fractional classical mechanics and the α-stable Lévy random process.The book is well-suited for theorists, pure and applied mathematicians, solid-state physicists, chemists, and others working with the Schrödinger equation, the path integral technique and applications of fractional calculus in various research areas. It is useful to skilled researchers as well as to graduate students looking for new ideas and advanced approaches.
