The Feynman Integral and Feynman's Operational Calculus PDF Download
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Author: Gerald W. Johnson
Publisher: Clarendon Press
ISBN: 0191546267
Category : Mathematics
Languages : en
Pages : 790
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Book Description
This 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.
Author: Gerald W. Johnson
Publisher: Clarendon Press
ISBN: 0191546267
Category : Mathematics
Languages : en
Pages : 790
Get Book Here
Book Description
This 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.
Author: Gerald W. Johnson
Publisher: Oxford University Press on Demand
ISBN: 9780198515722
Category : Mathematics
Languages : en
Pages : 771
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Book Description
This 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.
Author: Gerald W Johnson
Publisher: OUP Oxford
ISBN: 0191006882
Category : Science
Languages : en
Pages : 439
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Book Description
This book is aimed at providing a coherent, essentially self-contained, rigorous and comprehensive abstract theory of Feynman's operational calculus for noncommuting operators. Although it is inspired by Feynman's original heuristic suggestions and time-ordering rules in his seminal 1951 paper An operator calculus having applications in quantum electrodynamics, as will be made abundantly clear in the introduction (Chapter 1) and elsewhere in the text, the theory developed in this book also goes well beyond them in a number of directions which were not anticipated in Feynman's work. Hence, the second part of the main title of this book. The basic properties of the operational calculus are developed and certain algebraic and analytic properties of the operational calculus are explored. Also, the operational calculus will be seen to possess some pleasant stability properties. Furthermore, an evolution equation and a generalized integral equation obeyed by the operational calculus are discussed and connections with certain analytic Feynman integrals are noted. This volume is essentially self-contained and we only assume that the reader has a reasonable, graduate level, background in analysis, measure theory and functional analysis or operator theory. Much of the necessary remaining background is supplied in the text itself.
Author: Gerald W. Johnson
Publisher: American Mathematical Soc.
ISBN: 0821824139
Category : Mathematics
Languages : en
Pages : 88
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Book Description
The basic purpose of the paper is to construct, for the indicated integrals, series expansions in terms of finite multiple integrals of increasing multiplicity ("generalized Dyson series''). The authors study in detail the character of these expansions in the case when the measure [lowercase Greek]Eta = [lowercase Greek]Mu + [lowercase Greek]Nu contains, in addition to a continuous part [lowercase Greek]Mu, a discrete part [lowercase Greek]Nu as well. Using generalized Feynman diagrams they give a graphical description of the expansions obtained; they also describe the Banach algebra generated by the functionals under consideration and establish connections with Feynman's operational calculus.
Author: Nguyen Dinh Cong
Publisher: Oxford University Press
ISBN: 9780198501572
Category : Mathematics
Languages : en
Pages : 216
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Book Description
This book is the first systematic treatment of the theory of topological dynamics of random dynamical systems. A relatively new field, the theory of random dynamical systems unites and develops the classical deterministic theory of dynamical systems and probability theory, finding numerous applications in disciplines ranging from physics and biology to engineering, finance and economics. This book presents in detail the solutions to the most fundamental problems of topological dynamics: linearization of nonlinear smooth systems, classification, and structural stability of linear hyperbolic systems. Employing the tools and methods of algebraic ergodic theory, the theory presented in the book has surprisingly beautiful results showing the richness of random dynamical systems as well as giving a gentle generalization of the classical deterministic theory.
Author: Ian Anderson (Ph. D.)
Publisher: Oxford University Press
ISBN: 9780198500292
Category : Mathematics
Languages : en
Pages : 256
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Book Description
The mathematics of tournament design are surprisingly subtle, and this book, an extensively revised version of Ellis Horwood's popular Combinatorial Designs: Construction Methods, provides a thorough introduction. It includes a new chapter on league schedules, which discusses round robin tournaments, venue sequences, and carry-over effects. It also discusses balanced tournament designs, double schedules, and bridge and whist tournament design. Readable and authoritative, the book emphasizes throughout the historical development of the material and includes numerous examples and exercises giving detailed constructions.
Author: Klaus Gürlebeck
Publisher: John Wiley & Sons
ISBN:
Category : Mathematics
Languages : en
Pages : 392
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Book Description
Quarternionic calculus covers a branch of mathematics which uses computational techniques to help solve problems from a wide variety of physical systems which are mathematically modelled in 3, 4 or more dimensions. Examples of the application areas include thermodynamics, hydrodynamics, geophysics and structural mechanics. Focusing on the Clifford algebra approach the authors have drawn together the research into quarternionic calculus to provide the non-expert or research student with an accessible introduction to the subject. This book fills the gap between the theoretical representations and the requirements of the user.
Author: Sonia Mazzucchi
Publisher: World Scientific
ISBN: 9811214808
Category : Science
Languages : en
Pages : 360
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Book Description
Feynman path integrals are ubiquitous in quantum physics, even if a large part of the scientific community still considers them as a heuristic tool that lacks a sound mathematical definition. Our book aims to refute this prejudice, providing an extensive and self-contained description of the mathematical theory of Feynman path integration, from the earlier attempts to the latest developments, as well as its applications to quantum mechanics.This second edition presents a detailed discussion of the general theory of complex integration on infinite dimensional spaces, providing on one hand a unified view of the various existing approaches to the mathematical construction of Feynman path integrals and on the other hand a connection with the classical theory of stochastic processes. Moreover, new chapters containing recent applications to several dynamical systems have been added.This book bridges between the realms of stochastic analysis and the theory of Feynman path integration. It is accessible to both mathematicians and physicists.
Author: Alan F. Blackwell
Publisher: Springer Science & Business Media
ISBN: 9401735247
Category : Computers
Languages : en
Pages : 170
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Book Description
This book provides an introductory overview of the rapid growth in interdisciplinary research into Thinking with Diagrams. Diagrammatic representations are becoming more common in everyday human experience, yet they offer unique challenges to cognitive science research. Neither linguistic nor perceptual theories are sufficient to completely explain their advantages and applications. These research challenges may be part of the reason why so many diagrams are badly designed or badly used. This is ironic when the user interfaces of computer software and the worldwide web are becoming so completely dominated by graphical and diagrammatic representations. This book includes chapters commissioned from leading researchers in the major disciplines involved in diagrams research. They review the philosophical status of diagrams, the cognitive processes involved in their application, and a range of specialist fields in which diagrams are central, including education, architectural design and visual programming languages. The result is immediately relevant to researchers in cognitive science and artificial intelligence, as well as in applied technology areas such as human-computer interaction and information design.
Author: James K. Lindsey
Publisher: Oxford University Press
ISBN: 9780198523598
Category : Mathematics
Languages : en
Pages : 512
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Book Description
Two unifying components of statistics are the likelihood function and the exponential family. These are brought together for the first time as the central themes in this book on statistical inference, written for advanced undergraduate and graduate students in mathematical statistics.
