Feynman Integrals
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Feynman Integrals
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Author : Stefan Weinzierl
language : en
Publisher: Springer Nature
Release Date : 2022-06-11
Feynman Integrals written by Stefan Weinzierl and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-06-11 with Science categories.
This textbook on Feynman integrals starts from the basics, requiring only knowledge of special relativity and undergraduate mathematics. Feynman integrals are indispensable for precision calculations in quantum field theory. At the same time, they are also fascinating from a mathematical point of view. Topics from quantum field theory and advanced mathematics are introduced as needed. The book covers modern developments in the field of Feynman integrals. Topics included are: representations of Feynman integrals, integration-by-parts, differential equations, intersection theory, multiple polylogarithms, Gelfand-Kapranov-Zelevinsky systems, coactions and symbols, cluster algebras, elliptic Feynman integrals, and motives associated with Feynman integrals. This volume is aimed at a) students at the master's level in physics or mathematics, b) physicists who want to learn how to calculate Feynman integrals (for whom state-of-the-art techniques and computations are provided), and c) mathematicians who are interested in the mathematical aspects underlying Feynman integrals. It is, indeed, the interwoven nature of their physical and mathematical aspects that make Feynman integrals so enthralling.
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.
Homology And Feynman Integrals
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Author : Rudolph C. Hwa
language : en
Publisher:
Release Date : 1966
Homology And Feynman Integrals written by Rudolph C. Hwa and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1966 with Mathematics categories.
Evaluating Feynman Integrals
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Author : Vladimir A. Smirnov
language : en
Publisher: Springer
Release Date : 2005-02-28
Evaluating Feynman Integrals written by Vladimir A. Smirnov and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-02-28 with Science categories.
The problem of evaluating Feynman integrals over loop momenta has existed from the early days of perturbative quantum field theory. Although a great variety of methods for evaluating Feynman integrals has been developed over a span of more than fifty years, this book is a first attempt to summarize them. Evaluating Feynman Integrals characterizes the most powerful methods, in particular those used for recent, quite sophisticated calculations, and then illustrates them with numerous examples, starting from very simple ones and progressing to nontrivial examples.
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.
Analytic Tools For Feynman Integrals
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Author : Vladimir A. Smirnov
language : en
Publisher: Springer
Release Date : 2013-01-16
Analytic Tools For Feynman Integrals written by Vladimir A. Smirnov and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-01-16 with Science categories.
The goal of this book is to describe the most powerful methods for evaluating multiloop Feynman integrals that are currently used in practice. This book supersedes the author’s previous Springer book “Evaluating Feynman Integrals” and its textbook version “Feynman Integral Calculus.” Since the publication of these two books, powerful new methods have arisen and conventional methods have been improved on in essential ways. A further qualitative change is the fact that most of the methods and the corresponding algorithms have now been implemented in computer codes which are often public. In comparison to the two previous books, three new chapters have been added: One is on sector decomposition, while the second describes a new method by Lee. The third new chapter concerns the asymptotic expansions of Feynman integrals in momenta and masses, which were described in detail in another Springer book, “Applied Asymptotic Expansions in Momenta and Masses,” by the author. This chapter describes, on the basis of papers that appeared after the publication of said book, how to algorithmically discover the regions relevant to a given limit within the strategy of expansion by regions. In addition, the chapters on the method of Mellin-Barnes representation and on the method of integration by parts have been substantially rewritten, with an emphasis on the corresponding algorithms and computer codes.
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.
Quantum Mechanics And Path Integrals
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Author : Richard P. Feynman
language : en
Publisher: Courier Corporation
Release Date : 2010-07-21
Quantum Mechanics And Path Integrals written by Richard P. Feynman and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-07-21 with Science categories.
Looks at quantum mechanics, covering such topics as perturbation method, statistical mechanics, path integrals, and quantum electrodynamics.
Open Quantum Systems And Feynman Integrals
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Author : P. Exner
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Open Quantum Systems And Feynman Integrals written by P. Exner 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 2012-12-06 with Science categories.
Every part of physics offers examples of non-stability phenomena, but probably nowhere are they so plentiful and worthy of study as in the realm of quantum theory. The present volume is devoted to this problem: we shall be concerned with open quantum systems, i.e. those that cannot be regarded as isolated from the rest of the physical universe. It is a natural framework in which non-stationary processes can be investigated. There are two main approaches to the treatment of open systems in quantum theory. In both the system under consideration is viewed as part of a larger system, assumed to be isolated in a reasonable approximation. They are differentiated mainly by the way in which the state Hilbert space of the open system is related to that of the isolated system - either by orthogonal sum or by tensor product. Though often applicable simultaneously to the same physical situation, these approaches are complementary in a sense and are adapted to different purposes. Here we shall be concerned with the first approach, which is suitable primarily for a description of decay processes, absorption, etc. The second approach is used mostly for the treatment of various relaxation phenomena. It is comparably better examined at present; in particular, the reader may consult a monograph by E. B. Davies.
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.