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 | : J. B. Boyling |
Publisher | : |
Total Pages | : 41 |
Release | : 1967 |
Genre | : |
ISBN | : |
The methods of homology theory are applied to Feynman integrals in alpha-space. In the case of single-loop graphs the relevant relative homology groups are computed and the results compared with those obtained by k-space methods. For graphs with more than one loop the permanent pinch difficulty is overcome by modifying the ambient manifold and applying Thom's isotopy theorem. Pinching conditions are then found for Landau singularities in which complete circuits are contracted out and for mixed second-type singularities. The breakdown of the hierarchical principle in perturbation theory is also explained from this point of view. (Author).
Author | : Frédéric Pham |
Publisher | : Springer Science & Business Media |
Total Pages | : 218 |
Release | : 2011-04-22 |
Genre | : Mathematics |
ISBN | : 0857296035 |
Bringing together two fundamental texts from Frédéric Pham’s research on singular integrals, the first part of this book focuses on topological and geometrical aspects while the second explains the analytic approach. Using notions developed by J. Leray in the calculus of residues in several variables and R. Thom’s isotopy theorems, Frédéric Pham’s foundational study of the singularities of integrals lies at the interface between analysis and algebraic geometry, culminating in the Picard-Lefschetz formulae. These mathematical structures, enriched by the work of Nilsson, are then approached using methods from the theory of differential equations and generalized from the point of view of hyperfunction theory and microlocal analysis. Providing a ‘must-have’ introduction to the singularities of integrals, a number of supplementary references also offer a convenient guide to the subjects covered. This book will appeal to both mathematicians and physicists with an interest in the area of singularities of integrals. Frédéric Pham, now retired, was Professor at the University of Nice. He has published several educational and research texts. His recent work concerns semi-classical analysis and resurgent functions.
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.