Mathematical Feynman Path Integrals And Their Applications

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Mathematical Feynman Path Integrals And Their Applications Second Edition

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Author : Sonia Mazzucchi
language : en
Publisher: World Scientific
Release Date : 2021-11-16

Mathematical Feynman Path Integrals And Their Applications Second Edition 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 2021-11-16 with Science categories.

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.

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.

Path Integrals In Quantum Mechanics Statistics Polymer Physics And Financial Markets

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Author : Hagen Kleinert
language : en
Publisher: World Scientific
Release Date : 2009

Path Integrals In Quantum Mechanics Statistics Polymer Physics And Financial Markets written by Hagen Kleinert 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 Business & Economics categories.

Topological restrictions. These are relevant to the understanding of the statistical properties of elementary particles and the entanglement phenomena in polymer physics and biophysics. The Chern-Simons theory of particles with fractional statistics (anyons) is introduced and applied to explain the fractional quantum Hall effect." "The relevance of path integrals to financial markets is discussed, and improvements of the famous Black-Scholes formula for option prices are developed which account for the fact that large market fluctuations occur much more frequently than in Gaussian distributions." --Book Jacket.

Techniques And Applications Of Path Integration

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Author : L. S. Schulman
language : en
Publisher: Courier Corporation
Release Date : 2012-10-10

Techniques And Applications Of Path Integration written by L. S. Schulman and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-10-10 with Science categories.

Suitable for advanced undergraduates and graduate students, this text develops the techniques of path integration and deals with applications, covering a host of illustrative examples. 26 figures. 1981 edition.

Path Integral Methods And Their Applications

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Author :
language : en
Publisher: Allied Publishers
Release Date : 2002

Path Integral Methods And Their Applications written by and has been published by Allied Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with categories.

Path Integrals In Physics

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Author : M Chaichian
language : en
Publisher: CRC Press
Release Date : 2019-08-30

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 2019-08-30 with 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.

Path Integrals And Quantum Processes

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Author : Mark S. Swanson
language : en
Publisher: Academic Press
Release Date : 2012-12-02

Path Integrals And Quantum Processes written by Mark S. Swanson and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-02 with Science categories.

In a clearly written and systematic presentation, Path Integrals and Quantum Processes covers all concepts necessary to understand the path integral approach to calculating transition elements, partition functions, and source functionals. The book, which assumes only a familiarity with quantum mechanics, is ideal for use as a supplemental textbook in quantum mechanics and quantum field theory courses. Graduate and post-graduate students who are unfamiliar with the path integral will also benefit from this contemporary text. Exercise sets are interspersed throughout the text to facilitate self-study. - Explicates the relationship between the operator and path integral formulations of quantum mechanics and quantum field theory - Provides a systematic and detailed presentation of Grassmann variables - Covers Dirac's method of constraints and the relationship of ghosts, gauge invariance, and gauge conditions in gauge field theory - Includes applications to statistical mechanics, the effective action and potential, and anomaly analysis

Path Integrals And Anomalies In Curved Space

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Author : Fiorenzo Bastianelli
language : en
Publisher: Cambridge University Press
Release Date : 2006-07-20

Path Integrals And Anomalies In Curved Space written by Fiorenzo Bastianelli and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-07-20 with Science categories.

This book introduces path integrals, a powerful method for describing quantum phenomena, and then uses them to compute anomalies in quantum field theories. An advanced text for researchers and graduate students of quantum field theory and string theory, it also provides a stand-alone introduction to path integrals in quantum mechanics.

Equivariant Cohomology And Localization Of Path Integrals

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Author : Richard J. Szabo
language : en
Publisher: Springer Science & Business Media
Release Date : 2003-07-01

Equivariant Cohomology And Localization Of Path Integrals written by Richard J. Szabo 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 2003-07-01 with Science categories.

This book, addressing both researchers and graduate students, reviews equivariant localization techniques for the evaluation of Feynman path integrals. The author gives the relevant mathematical background in some detail, showing at the same time how localization ideas are related to classical integrability. The text explores the symmetries inherent in localizable models for assessing the applicability of localization formulae. Various applications from physics and mathematics are presented.

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.