Author : Barry Simon
Publisher : American Mathematical Soc.
Page : 322 pages
File Size : 34,55 MB
Release : 2005
Category : Mathematics
ISBN : 0821835823
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
Page : 292 pages
File Size : 26,33 MB
Release : 2010-11-08
Category : Mathematics
ISBN : 0817647910
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 : Pierre Cartier
Publisher : Cambridge University Press
Page : 7 pages
File Size : 35,24 MB
Release : 2006-11-30
Category : Science
ISBN : 1139462881
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 : Cécile Dewitt-Morette
Publisher : Springer Science & Business Media
Page : 436 pages
File Size : 15,21 MB
Release : 2013-11-11
Category : Science
ISBN : 1489903194
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 : Jean-Pierre Antoine
Publisher : Springer Science & Business Media
Page : 354 pages
File Size : 41,61 MB
Release : 2012-12-06
Category : Computers
ISBN : 1461570352
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 : Mark Iosifovich Freidlin
Publisher : Princeton University Press
Page : 560 pages
File Size : 19,69 MB
Release : 2016-03-02
Category : Mathematics
ISBN : 1400881595
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 : Klaus Bichteler
Publisher : Springer Science & Business Media
Page : 203 pages
File Size : 49,30 MB
Release : 2010-11-23
Category : Mathematics
ISBN : 303480055X
This book covers Lebesgue integration and its generalizations from Daniell's point of view, modified by the use of seminorms. Integrating functions rather than measuring sets is posited as the main purpose of measure theory. From this point of view Lebesgue's integral can be had as a rather straightforward, even simplistic, extension of Riemann's integral; and its aims, definitions, and procedures can be motivated at an elementary level. The notion of measurability, for example, is suggested by Littlewood's observations rather than being conveyed authoritatively through definitions of (sigma)-algebras and good-cut-conditions, the latter of which are hard to justify and thus appear mysterious, even nettlesome, to the beginner. The approach taken provides the additional benefit of cutting the labor in half. The use of seminorms, ubiquitous in modern analysis, speeds things up even further. The book is intended for the reader who has some experience with proofs, a beginning graduate student for example. It might even be useful to the advanced mathematician who is confronted with situations - such as stochastic integration - where the set-measuring approach to integration does not work.
Author : Barry Wacksman
Publisher : John Wiley & Sons
Page : 261 pages
File Size : 24,47 MB
Release : 2014-04-28
Category : Business & Economics
ISBN : 1118907213
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
Page : 284 pages
File Size : 13,52 MB
Release : 2014-02-20
Category : Technology & Engineering
ISBN : 146149320X
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 : A.D. Egorov
Publisher : Springer Science & Business Media
Page : 421 pages
File Size : 11,3 MB
Release : 2012-12-06
Category : Mathematics
ISBN : 9401117616
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.
