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Mathematical Theory Of Feynman Path Integrals
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Book Synopsis Mathematical Theory of Feynman Path Integrals by : Sergio A. Albeverio
Download or read book Mathematical Theory of Feynman Path Integrals written by Sergio A. Albeverio and published by Springer. This book was released on 2006-11-14 with total page 143 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Mathematical Theory of Feynman Path Integrals by : Sergio Albeverio
Download or read book Mathematical Theory of Feynman Path Integrals written by Sergio Albeverio and published by Springer. This book was released on 2008-05-06 with total page 182 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Mathematical Feynman Path Integrals and Their Applications by :
Download or read book Mathematical Feynman Path Integrals and Their Applications written by and published by . This book was released on with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Mathematical Feynman Path Integrals And Their Applications (Second Edition) by : Sonia Mazzucchi
Download or read book Mathematical Feynman Path Integrals And Their Applications (Second Edition) written by Sonia Mazzucchi and published by World Scientific. This book was released on 2021-11-16 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Mathematical Theory of Feynman Path Integrals by : Sergio A. Albeverio
Download or read book Mathematical Theory of Feynman Path Integrals written by Sergio A. Albeverio and published by . This book was released on 2014-09-01 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Handbook of Feynman Path Integrals by : Christian Grosche
Download or read book Handbook of Feynman Path Integrals written by Christian Grosche and published by . This book was released on 2014-01-15 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis The Feynman Integral and Feynman's Operational Calculus by : Gerald W. Johnson
Download or read book The Feynman Integral and Feynman's Operational Calculus written by Gerald W. Johnson and published by Clarendon Press. This book was released on 2000-03-16 with total page 790 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Mathematical Theory of Feynman Path Integrals by : Sergio Albeverio
Download or read book Mathematical Theory of Feynman Path Integrals written by Sergio Albeverio and published by . This book was released on 1974 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Feynman Path Integrals in Quantum Mechanics and Statistical Physics by : Lukong Cornelius Fai
Download or read book Feynman Path Integrals in Quantum Mechanics and Statistical Physics written by Lukong Cornelius Fai and published by CRC Press. This book was released on 2021-04-16 with total page 394 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Quantum Mechanics and Path Integrals [by] R.P. Feynman [and] A.R. Hibbs by : Richard Phillips Feynman
Download or read book Quantum Mechanics and Path Integrals [by] R.P. Feynman [and] A.R. Hibbs written by Richard Phillips Feynman and published by . This book was released on 1965 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Quantum Field Theory by : Lukong Cornelius Fai
Download or read book Quantum Field Theory written by Lukong Cornelius Fai and published by CRC Press. This book was released on 2019-06-20 with total page 440 pages. Available in PDF, EPUB and Kindle. Book excerpt: Choice Recommended Title, February 2020 This book explores quantum field theory using the Feynman functional and diagrammatic techniques as foundations to apply Quantum Field Theory to a broad range of topics in physics. This book will be of interest not only to condensed matter physicists but physicists in a range of disciplines as the techniques explored apply to high-energy as well as soft matter physics. 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
Book Synopsis Path Integrals and Quantum Processes by : Mark S. Swanson
Download or read book Path Integrals and Quantum Processes written by Mark S. Swanson and published by Courier Corporation. This book was released on 2014-02-19 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Mathematical Theory of Feynman Path Integrals by : Sergio A. Albeverio
Download or read book Mathematical Theory of Feynman Path Integrals written by Sergio A. Albeverio and published by . This book was released on 2008 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Quantum Gravitation by : Herbert W. Hamber
Download or read book Quantum Gravitation written by Herbert W. Hamber and published by Springer Science & Business Media. This book was released on 2008-10-20 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Quantum Gravitation" approaches the subject from the point of view of Feynman path integrals, which provide a manifestly covariant approach in which fundamental quantum aspects of the theory such as radiative corrections and the renormalization group can be systematically and consistently addressed. It is shown that the path integral method is suitable for both perturbative as well as non-perturbative studies, and is already known to offer a framework for the theoretical investigation of non-Abelian gauge theories, the basis for three of the four known fundamental forces in nature. The book thus provides a coherent outline of the present status of the theory gravity based on Feynman’s formulation, with an emphasis on quantitative results. Topics are organized in such a way that the correspondence to similar methods and results in modern gauge theories becomes apparent. Covariant perturbation theory are developed using the full machinery of Feynman rules, gauge fixing, background methods and ghosts. The renormalization group for gravity and the existence of non-trivial ultraviolet fixed points are investigated, stressing a close correspondence with well understood statistical field theory models. The final chapter addresses contemporary issues in quantum cosmology such as scale dependent gravitational constants and quantum effects in the early universe.
Book Synopsis Techniques and Applications of Path Integration by : L. S. Schulman
Download or read book Techniques and Applications of Path Integration written by L. S. Schulman and published by Courier Corporation. This book was released on 2012-10-10 with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Rigorous Time Slicing Approach to Feynman Path Integrals by : Daisuke Fujiwara
Download or read book Rigorous Time Slicing Approach to Feynman Path Integrals written by Daisuke Fujiwara and published by Springer. This book was released on 2017-06-24 with total page 333 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Feynman's Thesis by : Richard Phillips Feynman
Download or read book Feynman's Thesis written by Richard Phillips Feynman and published by World Scientific. This book was released on 2005 with total page 142 pages. Available in PDF, EPUB and Kindle. Book excerpt: Richard Feynman's never previously published doctoral thesis formed the heart of much of his brilliant and profound work in theoretical physics. Entitled ?The Principle of Least Action in Quantum Mechanics," its original motive was to quantize the classical action-at-a-distance electrodynamics. Because that theory adopted an overall space?time viewpoint, the classical Hamiltonian approach used in the conventional formulations of quantum theory could not be used, so Feynman turned to the Lagrangian function and the principle of least action as his points of departure.The result was the path integral approach, which satisfied ? and transcended ? its original motivation, and has enjoyed great success in renormalized quantum field theory, including the derivation of the ubiquitous Feynman diagrams for elementary particles. Path integrals have many other applications, including atomic, molecular, and nuclear scattering, statistical mechanics, quantum liquids and solids, Brownian motion, and noise theory. It also sheds new light on fundamental issues like the interpretation of quantum theory because of its new overall space?time viewpoint.The present volume includes Feynman's Princeton thesis, the related review article ?Space?Time Approach to Non-Relativistic Quantum Mechanics? [Reviews of Modern Physics 20 (1948), 367?387], Paul Dirac's seminal paper ?The Lagrangian in Quantum Mechanics'' [Physikalische Zeitschrift der Sowjetunion, Band 3, Heft 1 (1933)], and an introduction by Laurie M Brown.
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