Feynman Integrals

Author : Vladimir A. Smirnov
Publisher : Springer
Page : 251 pages
File Size : 41,8 Mb
Release : 2005-02-28
Category : Science
ISBN : 9783540447030

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Evaluating Feynman Integrals by Vladimir A. Smirnov Pdf

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.

Author : Vladimir A. Smirnov
Publisher : Springer
Page : 299 pages
File Size : 51,7 Mb
Release : 2013-01-16
Category : Science
ISBN : 9783642348860

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Analytic Tools for Feynman Integrals by Vladimir A. Smirnov Pdf

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.

Author : Sergio A. Albeverio,Raphael J. Høegh-Krohn
Publisher : Springer
Page : 143 pages
File Size : 46,7 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 : Stefan Weinzierl
Publisher : Springer Nature
Page : 852 pages
File Size : 45,7 Mb
Release : 2022-06-11
Category : Science
ISBN : 9783030995584

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Feynman Integrals by Stefan Weinzierl Pdf

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.

Author : P. Exner
Publisher : Springer Science & Business Media
Page : 374 pages
File Size : 41,5 Mb
Release : 2012-12-06
Category : Science
ISBN : 9789400952072

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Open Quantum Systems and Feynman Integrals by P. Exner Pdf

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.

Author : Vladimir A. Smirnov
Publisher : Springer Science & Business Media
Page : 288 pages
File Size : 47,5 Mb
Release : 2006-08-02
Category : Mathematics
ISBN : 9783540306108

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Feynman Integral Calculus by Vladimir A. Smirnov Pdf

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.

Author : Richard Phillips Feynman
Publisher : Unknown
Page : 0 pages
File Size : 45,8 Mb
Release : 1965
Category : Quantum theory
ISBN : 0071139486

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Quantum Mechanics and Path Integrals [by] R.P. Feynman [and] A.R. Hibbs by Richard Phillips Feynman Pdf

Author : Noboru Nakanishi
Publisher : Routledge
Page : 244 pages
File Size : 47,7 Mb
Release : 1971
Category : Mathematics
ISBN : UOM:39015015160297

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Graph Theory and Feynman Integrals by Noboru Nakanishi Pdf

Author : Sergio Albeverio,Rafael Høegh-Krohn,Sonia Mazzucchi
Publisher : Springer Science & Business Media
Page : 184 pages
File Size : 45,9 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 : Sonia Mazzucchi
Publisher : World Scientific
Page : 360 pages
File Size : 54,5 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 : Gerald W. Johnson,Michel L. Lapidus
Publisher : Clarendon Press
Page : 790 pages
File Size : 45,9 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 : Christian Grosche,Frank Steiner
Publisher : Unknown
Page : 464 pages
File Size : 55,7 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 : 52,5 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 : Valerio Tognetti,Roberto Casalbuoni,Riccardo Giachetti,Ruggero Vaia,Paola Verrucchi
Publisher : World Scientific
Page : 642 pages
File Size : 43,7 Mb
Release : 1999-04-01
Category : Electronic
ISBN : 9789814543842

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Path Integrals From Pev To Tev: 50 Years After Feynman's Paper - Proceedings Of The Sixth International Conference by Valerio Tognetti,Roberto Casalbuoni,Riccardo Giachetti,Ruggero Vaia,Paola Verrucchi Pdf

This book contains the invited contributions to the 6th International Conference on Path Integrals from peV to TeV, held in Florence in 1998. The conference, devoted to functional integration, brought together many physicists with interests ranging from elementary particles to nuclear, solid state, liquid state, polymer and complex systems physics. The variety of topics is reflected in the book, which is a unique collection of papers on manifold applications of functional methods in several areas of physics.

Author : Anonim
Publisher : Unknown
Page : 128 pages
File Size : 45,9 Mb
Release : 2024-07-01
Category : Electronic
ISBN : 9789814469272

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Mathematical Feynman Path Integrals and Their Applications by Anonim Pdf