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Mathematical Theory Of Feynman Path Integrals

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Mathematical Theory Of Feynman Path Integrals

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Author : Sergio Albeverio
language : en
Publisher: Springer
Release Date : 2008-05-06

Mathematical Theory Of Feynman Path Integrals written by Sergio Albeverio and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-05-06 with Mathematics categories.

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.

Mathematical Theory Of Feynman Path Integrals

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Author : Sergio A. Albeverio
language : en
Publisher: Springer
Release Date : 2006-11-14

Mathematical Theory Of Feynman Path Integrals written by Sergio A. Albeverio and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.

Feynman path integrals integrals, suggested heuristically by Feynman in the 40s, have become the basis of much of contemporary physics, from non relativistic quantum mechanics to quantum fields, including gauge fields, gravitation, cosmology. Recently ideas based on Feynman path integrals have also played an important role in areas of mathematics like low dimensional topology and differential geometry, algebraic geometry, infinite dimensional analysis and geometry, and number theory. 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. To take care of the many developments which have occurred since then, an entire new chapter about the current forefront of research has been added. Except for this new chapter, the basic material and presentation of the first edition was mantained, a few misprints have been corrected. At the end of each chapter the reader will also find notes with further bibliographical information.

Mathematical Theory Of Feynman Path Integrals

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Author : Sergio A. Albeverio
language : en
Publisher:
Release Date : 2014-09-01

Mathematical Theory Of Feynman Path Integrals written by Sergio A. Albeverio and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-09-01 with categories.

Mathematical Theory Of Feynman Path Integrals

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Author : Sergio Albeverio
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-05-30

Mathematical Theory Of Feynman Path Integrals written by Sergio Albeverio and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-05-30 with Mathematics categories.

Mathematical Theory Of Feynman Path Integrals

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Author : Sergio Albeverio
language : en
Publisher: Springer
Release Date : 1976-01-01

Mathematical Feynman Path Integrals And Their Applications

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Author : Sonia Mazzucchi
language : en
Publisher: World Scientific
Release Date : 2009

Mathematical Feynman Path Integrals And Their Applications written by Sonia Mazzucchi and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Mathematics categories.

Although more than 60 years have passed since their first appearance, Feynman path integrals have yet to lose their fascination and luster. They are not only a formidable instrument of theoretical physics, but also a mathematical challenge; in fact, several mathematicians in the last 40 years have devoted their efforts to the rigorous mathematical definition of Feynman''s ideas. This volume provides a detailed, self-contained description of the mathematical difficulties as well as the possible techniques used to solve these difficulties. In particular, it gives a complete overview of the mathematical realization of Feynman path integrals in terms of well-defined functional integrals, that is, the infinite dimensional oscillatory integrals. It contains the traditional results on the topic as well as the more recent developments obtained by the author. Mathematical Feynman Path Integrals and Their Applications is devoted to both mathematicians and physicists, graduate students and researchers who are interested in the problem of mathematical foundations of Feynman path integrals.

Quantum Field Theory

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Author : Bertfried Fauser
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-06-02

Quantum Field Theory written by Bertfried Fauser and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-06-02 with Science categories.

The present volume emerged from the 3rd `Blaubeuren Workshop: Recent Developments in Quantum Field Theory', held in July 2007 at the Max Planck Institute of Mathematics in the Sciences in Leipzig/Germany. All of the contributions are committed to the idea of this workshop series: To bring together outstanding experts working in the field of mathematics and physics to discuss in an open atmosphere the fundamental questions at the frontier of theoretical physics.

The Feynman Integral And Feynman S Operational Calculus

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Author :
language : en
Publisher: OUP Oxford
Release Date : 2000-03-16

The Feynman Integral And Feynman S Operational Calculus written by and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-03-16 with Mathematics categories.

The aim of this book is to make accessible to mathematicians, physicists and other scientists interested in qunatum theory, the beautiful but mathematically difficult subjects of the Feynman integral and Feynman's operational calculus. Some advantages of the approaches to the Feynman integral which are treated in detail in this book are the following: the existence of the Feynman integral is established for very general potentials in all four cases; under more restrictive but still broad conditions, three of these Feynman integrals agree with one another and with the unitary group from the usual approach to quantum dynamics; these same three Feynman integrals possess pleasant stability properties. Much of the material covered here was previously available only in the research literature, and the book also contains some new results. The background material in mathematics and physics that motivates the study of the Feynman integral and Feynman's operational calculus is discussed, and detailed proofs are provided for the central results.

Rigorous Time Slicing Approach To Feynman Path Integrals

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Author : Daisuke Fujiwara
language : en
Publisher: Springer
Release Date : 2017-06-24

Rigorous Time Slicing Approach To Feynman Path Integrals written by Daisuke Fujiwara and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-06-24 with Science categories.

This book proves that Feynman's original definition of the path integral actually converges to the fundamental solution of the Schrödinger equation at least in the short term if the potential is differentiable sufficiently many times and its derivatives of order equal to or higher than two are bounded. The semi-classical asymptotic formula up to the second term of the fundamental solution is also proved by a method different from that of Birkhoff. A bound of the remainder term is also proved.The Feynman path integral is a method of quantization using the Lagrangian function, whereas Schrödinger's quantization uses the Hamiltonian function. These two methods are believed to be equivalent. But equivalence is not fully proved mathematically, because, compared with Schrödinger's method, there is still much to be done concerning rigorous mathematical treatment of Feynman's method. Feynman himself defined a path integral as the limit of a sequence of integrals over finite-dimensional spaces which is obtained by dividing the time interval into small pieces. This method is called the time slicing approximation method or the time slicing method.This book consists of two parts. Part I is the main part. The time slicing method is performed step by step in detail in Part I. The time interval is divided into small pieces. Corresponding to each division a finite-dimensional integral is constructed following Feynman's famous paper. This finite-dimensional integral is not absolutely convergent. Owing to the assumption of the potential, it is an oscillatory integral. The oscillatory integral techniques developed in the theory of partial differential equations are applied to it. It turns out that the finite-dimensional integral gives a finite definite value. The stationary phase method is applied to it. Basic properties of oscillatory integrals and the stationary phase method are explained in the book in detail.Those finite-dimensional integrals form a sequence of approximation of the Feynman path integral when the division goes finer and finer. A careful discussion is required to prove the convergence of the approximate sequence as the length of each of the small subintervals tends to 0. For that purpose the book uses the stationary phase method of oscillatory integrals over a space of large dimension, of which the detailed proof is given in Part II of the book. By virtue of this method, the approximate sequence converges to the limit. This proves that the Feynman path integral converges. It turns out that the convergence occurs in a very strong topology. The fact that the limit is the fundamental solution of the Schrödinger equation is proved also by the stationary phase method. The semi-classical asymptotic formula naturally follows from the above discussion.A prerequisite for readers of this book is standard knowledge of functional analysis. Mathematical techniques required here are explained and proved from scratch in Part II, which occupies a large part of the book, because they are considerably different from techniques usually used in treating the Schrödinger equation.

Path Integrals In Physics

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Author : M Chaichian
language : en
Publisher: CRC Press
Release Date : 2018-10-03

Path Integrals In Physics written by M Chaichian and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-10-03 with Science categories.

Path Integrals in Physics: Volume I, Stochastic Processes and Quantum Mechanics presents the fundamentals of path integrals, both the Wiener and Feynman type, and their many applications in physics. Accessible to a broad community of theoretical physicists, the book deals with systems possessing a infinite number of degrees in freedom. It discusses the general physical background and concepts of the path integral approach used, followed by a detailed presentation of the most typical and important applications as well as problems with either their solutions or hints how to solve them. It describes in detail various applications, including systems with Grassmann variables. Each chapter is self-contained and can be considered as an independent textbook. The book provides a comprehensive, detailed, and systematic account of the subject suitable for both students and experienced researchers.

Mathematical Theory Of Feynman Path Integrals

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