Mathematical Theory Of Feynman Path Integrals

Author : Sergio Albeverio,Rafael Høegh-Krohn,Sonia Mazzucchi
Publisher : Springer
Page : 182 pages
File Size : 47,9 Mb
Release : 2008-05-06
Category : Mathematics
ISBN : 9783540769569

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Mathematical Theory of Feynman Path Integrals by Sergio Albeverio,Rafael Høegh-Krohn,Sonia Mazzucchi Pdf

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.

Author : Sergio A. Albeverio,Raphael J. Høegh-Krohn
Publisher : Springer
Page : 143 pages
File Size : 40,9 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540382508

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Mathematical Theory of Feynman Path Integrals by Sergio A. Albeverio,Raphael J. Høegh-Krohn Pdf

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.

Author : Sonia Mazzucchi
Publisher : World Scientific
Page : 360 pages
File Size : 50,7 Mb
Release : 2021-11-16
Category : Science
ISBN : 9789811214806

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Mathematical Feynman Path Integrals And Their Applications (Second Edition) by Sonia Mazzucchi Pdf

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 : Sergio A. Albeverio,Raphael J. Hoegh-Krohn
Publisher : Unknown
Page : 196 pages
File Size : 47,6 Mb
Release : 2014-09-01
Category : Electronic
ISBN : 3662177633

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Mathematical Theory of Feynman Path Integrals by Sergio A. Albeverio,Raphael J. Hoegh-Krohn Pdf

Author : Sergio Albeverio,Raphael Höegh-Krohn
Publisher : Unknown
Page : 252 pages
File Size : 52,9 Mb
Release : 1974
Category : Feynman integrals
ISBN : 8255301933

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Mathematical Theory of Feynman Path Integrals by Sergio Albeverio,Raphael Höegh-Krohn Pdf

Author : Sergio A. Albeverio,Raphael J. Høegh-Krohn,Sonia Mazzucchi
Publisher : Unknown
Page : 0 pages
File Size : 42,6 Mb
Release : 2008
Category : Functional analysis
ISBN : 8354076954

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Mathematical Theory of Feynman Path Integrals by Sergio A. Albeverio,Raphael J. Høegh-Krohn,Sonia Mazzucchi Pdf

Feynman path 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 since then, 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.

Author : Anonim
Publisher : Unknown
Page : 128 pages
File Size : 48,9 Mb
Release : 2024-06-25
Category : Electronic
ISBN : 9789814469272

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Mathematical Feynman Path Integrals and Their Applications by Anonim Pdf

Author : Sergio Albeverio,Rafael Høegh-Krohn,Sonia Mazzucchi
Publisher : Springer Science & Business Media
Page : 184 pages
File Size : 53,8 Mb
Release : 2008-05-30
Category : Mathematics
ISBN : 9783540769545

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Mathematical Theory of Feynman Path Integrals by Sergio Albeverio,Rafael Høegh-Krohn,Sonia Mazzucchi Pdf

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.

Author : Christian Grosche,Frank Steiner
Publisher : Unknown
Page : 464 pages
File Size : 52,9 Mb
Release : 2014-01-15
Category : Electronic
ISBN : 3662147602

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Handbook of Feynman Path Integrals by Christian Grosche,Frank Steiner Pdf

Author : Lukong Cornelius Fai
Publisher : CRC Press
Page : 394 pages
File Size : 47,9 Mb
Release : 2021-04-16
Category : Science
ISBN : 9781000349061

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Feynman Path Integrals in Quantum Mechanics and Statistical Physics by Lukong Cornelius Fai Pdf

This book provides an ideal introduction to the use of Feynman path integrals in the fields of quantum mechanics and statistical physics. It is written for graduate students and researchers in physics, mathematical physics, applied mathematics as well as chemistry. The material is presented in an accessible manner for readers with little knowledge of quantum mechanics and no prior exposure to path integrals. It begins with elementary concepts and a review of quantum mechanics that gradually builds the framework for the Feynman path integrals and how they are applied to problems in quantum mechanics and statistical physics. Problem sets throughout the book allow readers to test their understanding and reinforce the explanations of the theory in real situations. Features: Comprehensive and rigorous yet, presents an easy-to-understand approach. Applicable to a wide range of disciplines. Accessible to those with little, or basic, mathematical understanding.

Author : Gerald W. Johnson,Michel L. Lapidus
Publisher : Clarendon Press
Page : 790 pages
File Size : 44,7 Mb
Release : 2000-03-16
Category : Mathematics
ISBN : 9780191546266

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The Feynman Integral and Feynman's Operational Calculus by Gerald W. Johnson,Michel L. Lapidus Pdf

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 : Fabio Nicola,S. Ivan Trapasso
Publisher : Springer Nature
Page : 220 pages
File Size : 44,7 Mb
Release : 2022-07-28
Category : Science
ISBN : 9783031061868

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Wave Packet Analysis of Feynman Path Integrals by Fabio Nicola,S. Ivan Trapasso Pdf

The purpose of this monograph is to offer an accessible and essentially self-contained presentation of some mathematical aspects of the Feynman path integral in non-relativistic quantum mechanics. In spite of the primary role in the advancement of modern theoretical physics and the wide range of applications, path integrals are still a source of challenging problem for mathematicians. From this viewpoint, path integrals can be roughly described in terms of approximation formulas for an operator (usually the propagator of a Schrödinger-type evolution equation) involving a suitably designed sequence of operators. In keeping with the spirit of harmonic analysis, the guiding theme of the book is to illustrate how the powerful techniques of time-frequency analysis - based on the decomposition of functions and operators in terms of the so-called Gabor wave packets – can be successfully applied to mathematical path integrals, leading to remarkable results and paving the way to a fruitful interaction. This monograph intends to build a bridge between the communities of people working in time-frequency analysis and mathematical/theoretical physics, and to provide an exposition of the present novel approach along with its basic toolkit. Having in mind a researcher or a Ph.D. student as reader, we collected in Part I the necessary background, in the most suitable form for our purposes, following a smooth pedagogical pattern. Then Part II covers the analysis of path integrals, reflecting the topics addressed in the research activity of the authors in the last years.

Author : Daisuke Fujiwara
Publisher : Springer
Page : 333 pages
File Size : 53,7 Mb
Release : 2017-06-24
Category : Science
ISBN : 9784431565536

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Rigorous Time Slicing Approach to Feynman Path Integrals by Daisuke Fujiwara Pdf

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.

Author : Mark S. Swanson
Publisher : Courier Corporation
Page : 464 pages
File Size : 42,7 Mb
Release : 2014-02-19
Category : Science
ISBN : 9780486782300

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Path Integrals and Quantum Processes by Mark S. Swanson Pdf

Graduate-level, systematic presentation of path integral approach to calculating transition elements, partition functions, and source functionals. Covers Grassmann variables, field and gauge field theory, perturbation theory, and nonperturbative results. 1992 edition.

Author : M Chaichian,A Demichev
Publisher : CRC Press
Page : 368 pages
File Size : 55,5 Mb
Release : 2001-07-01
Category : Science
ISBN : 0750308028

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Path Integrals in Physics by M Chaichian,A Demichev Pdf

The path integral approach has proved extremely useful for the understanding of the most complex problems in quantum field theory, cosmology, and condensed matter physics. Path Integrals in Physics: Volume II, Quantum Field Theory, Statistical Physics and other Modern Applications covers the fundamentals of path integrals, both the Wiener and Feynman types, and their many applications in physics. The book deals with systems that have an infinite number of degrees of 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. Each chapter is self-contained and can be considered as an independent textbook. It provides a comprehensive, detailed, and systematic account of the subject suitable for both students and experienced researchers.