Generalized Dyson Series, Generalized Feynman Diagrams, the Feynman Integral and Feynman's Operational Calculus

Generalized Dyson Series, Generalized Feynman Diagrams, the Feynman Integral and Feynman's Operational Calculus PDF 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.

Generalized Dyson Series, Generalized Feynman Diagrams, the Feynman Integral and Feynman's Operational Calculus

Generalized Dyson Series, Generalized Feynman Diagrams, the Feynman Integral and Feynman's Operational Calculus PDF 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.

The Feynman Integral and Feynman's Operational Calculus

The Feynman Integral and Feynman's Operational Calculus PDF 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.

Feynman's Operational Calculus and Beyond

Feynman's Operational Calculus and Beyond PDF 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.

Mathematical Theory of Feynman Path Integrals

Mathematical Theory of Feynman Path Integrals PDF Author: Sergio Albeverio
Publisher: Springer Science & Business Media
ISBN: 3540769544
Category : Mathematics
Languages : en
Pages : 184

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Book Description
The 2nd edition of LNM 523 is based on the two first authors' mathematical approach of this theory presented in its 1st edition in 1976. An entire new chapter on the current forefront of research has been added. Except for this new chapter and the correction of a few misprints, the basic material and presentation of the first edition has been maintained. At the end of each chapter the reader will also find notes with further bibliographical information.

The Feynman Integral and Feynman's Operational Calculus

The Feynman Integral and Feynman's Operational Calculus PDF 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.

Stochastic Analysis And Mathematical Physics (Samp/anestoc 2002)

Stochastic Analysis And Mathematical Physics (Samp/anestoc 2002) PDF Author: Rolando Rebolledo
Publisher: World Scientific
ISBN: 9814481637
Category : Science
Languages : en
Pages : 313

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Book Description
The book collects a series of papers centered on two main streams: Feynman path integral approach to Quantum Mechanics and statistical mechanics of quantum open systems. Key authors discuss the state-of-the-art within their fields of expertise. In addition, the volume includes a number of contributed papers with new results, which have been thoroughly refereed.The contributions in this volume highlight emergent research in the area of stochastic analysis and mathematical physics, focusing, in particular on Feynman functional integral approach and, on the other hand, in quantum probability. The book is addressed to an audience of mathematical physicists, as well as specialists in probability theory, stochastic analysis and operator algebras.The proceedings have been selected for coverage in:• Index to Scientific & Technical Proceedings (ISTP CDROM version / ISI Proceedings)• CC Proceedings — Engineering & Physical Sciences

Gaussian Random Fields - Proceedings Of The Third Nagayo Levy Seminar

Gaussian Random Fields - Proceedings Of The Third Nagayo Levy Seminar PDF Author: Kazufumi Ito
Publisher: World Scientific
ISBN: 9814569372
Category :
Languages : en
Pages : 450

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Book Description
These proceedings emphasize new mathematical problems discussed in line with white noise analysis. Many papers deal with mathematical questions arising from actual phenomena. Various applications to stochastic differential equations, quantum field theory, functional integration such as Feynman integrals, limit theorems in probability are also discussed.

Ideas and Methods in Mathematical Analysis, Stochastics, and Applications: Volume 1

Ideas and Methods in Mathematical Analysis, Stochastics, and Applications: Volume 1 PDF Author: Sergio Albeverio
Publisher: Cambridge University Press
ISBN: 9780521419291
Category : Mathematics
Languages : en
Pages : 528

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Book Description
A collection of essays by many of the closest co-workers of Raphael Høegh-Krohn.

Journal of the Korean Mathematical Society

Journal of the Korean Mathematical Society PDF Author:
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 750

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Book Description


Referativnyĭ zhurnal

Referativnyĭ zhurnal PDF Author:
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 632

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Book Description