A Simple Definition Of The Feynman Integral With Applications
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A Simple Definition Of The Feynman Integral With Applications
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Author : Robert Horton Cameron
language : en
Publisher:
Release Date : 1983
A Simple Definition Of The Feynman Integral With Applications written by Robert Horton Cameron and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1983 with Feynman integrals categories.
A Simple Definition Of The Feynman Integral With Applications
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Author : Robert Horton Cameron
language : en
Publisher: American Mathematical Soc.
Release Date : 1983
A Simple Definition Of The Feynman Integral With Applications written by Robert Horton Cameron and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1983 with Feynman integral categories.
This memoir presents a simple sequential definition of the Feynman integral which is applicable to a rather large class of functionals.
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 Science 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.
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.
Definitions And Selected Applications Of Feynman Type Integrals
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Author : Jan Tarski
language : en
Publisher:
Release Date : 1974
Definitions And Selected Applications Of Feynman Type Integrals written by Jan Tarski and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1974 with categories.
Feynman Integral Calculus
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Author : Vladimir A. Smirnov
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-08-02
Feynman Integral Calculus written by Vladimir A. Smirnov 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 2006-08-02 with Mathematics categories.
The goal of the book is to summarize those methods for evaluating Feynman integrals that have been developed over a span of more than fifty years. The book characterizes the most powerful methods and illustrates them with numerous examples starting from very simple ones and progressing to nontrivial examples. The book demonstrates how to choose adequate methods and combine evaluation methods in a non-trivial way. The most powerful methods are characterized and then illustrated through numerous examples. This is an updated textbook version of the previous book (Evaluating Feynman integrals, STMP 211) of the author.
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.
The Feynman Integral And Feynman S Operational Calculus
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Author : Gerald W. Johnson
language : en
Publisher: Clarendon Press
Release Date : 2000-03-16
The Feynman Integral And Feynman S Operational Calculus written by Gerald W. Johnson and has been published by Clarendon Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-03-16 with Mathematics categories.
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.
Path Integrals In Quantum Mechanics Statistics Polymer Physics And Financial Markets
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Author : Hagen Kleinert
language : en
Publisher: World Scientific Publishing Company
Release Date : 2006-07-19
Path Integrals In Quantum Mechanics Statistics Polymer Physics And Financial Markets written by Hagen Kleinert and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-07-19 with Science categories.
This is the fourth, expanded edition of the comprehensive textbook published in 1990 on the theory and applications of path integrals. It is the first book to explicitly solve path integrals of a wide variety of nontrivial quantum-mechanical systems, in particular the hydrogen atom. The solutions have become possible by two major advances. The first is a new euclidean path integral formula which increases the restricted range of applicability of Feynman's famous formula to include singular attractive 1/r and 1/r2 potentials. The second is a simple quantum equivalence principle governing the transformation of euclidean path integrals to spaces with curvature and torsion, which leads to time-sliced path integrals that are manifestly invariant under coordinate transformations. In addition to the time-sliced definition, the author gives a perturbative definition of path integrals which makes them invariant under coordinate transformations. A consistent implementation of this property leads to an extension of the theory of generalized functions by defining uniquely integrals over products of distributions. The powerful Feynman–Kleinert variational approach is explained and developed systematically into a variational perturbation theory which, in contrast to ordinary perturbation theory, produces convergent expansions. The convergence is uniform from weak to strong couplings, opening a way to precise approximate evaluations of analytically unsolvable path integrals. Tunneling processes are treated in detail. The results are used to determine the lifetime of supercurrents, the stability of metastable thermodynamic phases, and the large-order behavior of perturbation expansions. A new variational treatment extends the range of validity of previous tunneling theories from large to small barriers. A corresponding extension of large-order perturbation theory also applies now to small orders. Special attention is devoted to path integrals with 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 given which account for the fact that large market fluctuations occur much more frequently than in the commonly used Gaussian distributions. The author's other book on ‘Critical Properties of φ4 Theories’ gives a thorough introduction to the field of critical phenomena and develops new powerful resummation techniques for the extraction of physical results from the divergent perturbation expansions.
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.
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.