Homology and Feynman Integrals
Author | : Rudolph C. Hwa |
Publisher | : |
Total Pages | : 352 |
Release | : 1966 |
Genre | : Mathematics |
ISBN | : |
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Author | : Rudolph C. Hwa |
Publisher | : |
Total Pages | : 352 |
Release | : 1966 |
Genre | : Mathematics |
ISBN | : |
Author | : Siegfried Engelmann |
Publisher | : |
Total Pages | : |
Release | : 1966 |
Genre | : |
ISBN | : |
Author | : Chia-Chao Hua |
Publisher | : |
Total Pages | : 331 |
Release | : 1966 |
Genre | : |
ISBN | : |
Author | : Stefan Weinzierl |
Publisher | : Springer Nature |
Total Pages | : 852 |
Release | : 2022-06-11 |
Genre | : Science |
ISBN | : 3030995585 |
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 | : Vladimir A. Smirnov |
Publisher | : Springer Science & Business Media |
Total Pages | : 288 |
Release | : 2006-08-02 |
Genre | : Mathematics |
ISBN | : 3540306102 |
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 | : Vladimir A. Smirnov |
Publisher | : Springer |
Total Pages | : 251 |
Release | : 2005-02-28 |
Genre | : Science |
ISBN | : 3540447032 |
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 | : Robert Horton Cameron |
Publisher | : American Mathematical Soc. |
Total Pages | : 53 |
Release | : 1983 |
Genre | : Feynman integral |
ISBN | : 0821822888 |
This memoir presents a simple sequential definition of the Feynman integral which is applicable to a rather large class of functionals.
Author | : Vladimir A. Smirnov |
Publisher | : Springer |
Total Pages | : 299 |
Release | : 2013-01-16 |
Genre | : Science |
ISBN | : 3642348866 |
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 | : Gerald W. Johnson |
Publisher | : Clarendon Press |
Total Pages | : 790 |
Release | : 2000-03-16 |
Genre | : Mathematics |
ISBN | : 0191546267 |
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 | : Sonia Mazzucchi |
Publisher | : World Scientific |
Total Pages | : 225 |
Release | : 2009-05-22 |
Genre | : Science |
ISBN | : 9814469270 |
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.