Numerical Integration Of Massive Two Loop Mellin Barnes Integrals In Minkowskian Regions
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| Author | : Ievgen Dubovyk |
| Publisher | : Springer Nature |
| Total Pages | : 296 |
| Release | : 2022-12-15 |
| Genre | : Science |
| ISBN | : 3031142721 |
In this book, the authors discuss the Mellin-Barnes representation of complex multidimensional integrals. Experiments frontiered by the High-Luminosity Large Hadron Collider at CERN and future collider projects demand the development of computational methods to achieve the theoretical precision required by experimental setups. In this regard, performing higher-order calculations in perturbative quantum field theory is of paramount importance. The Mellin-Barnes integrals technique has been successfully applied to the analytic and numerical analysis of integrals connected with virtual and real higher-order perturbative corrections to particle scattering. Easy-to-follow examples with the supplemental online material introduce the reader to the construction and the analytic, approximate, and numeric solution of Mellin-Barnes integrals in Euclidean and Minkowskian kinematic regimes. It also includes an overview of the state-of-the-art software packages for manipulating and evaluating Mellin-Barnes integrals. The book is meant for advanced students and young researchers to master the theoretical background needed to perform perturbative quantum field theory calculations.
| Author | : R. B. Paris |
| Publisher | : Cambridge University Press |
| Total Pages | : 452 |
| Release | : 2001-09-24 |
| Genre | : Mathematics |
| ISBN | : 9781139430128 |
Asymptotics and Mellin-Barnes Integrals, first published in 2001, provides an account of the use and properties of a type of complex integral representation that arises frequently in the study of special functions typically of interest in classical analysis and mathematical physics. After developing the properties of these integrals, their use in determining the asymptotic behaviour of special functions is detailed. Although such integrals have a long history, the book's account includes recent research results in analytic number theory and hyperasymptotics. The book also fills a gap in the literature on asymptotic analysis and special functions by providing a thorough account of the use of Mellin-Barnes integrals that is otherwise not available in other standard references on asymptotics.
| Author | : R. J. Eden |
| Publisher | : Cambridge University Press |
| Total Pages | : 300 |
| Release | : 2002-04-30 |
| Genre | : Mathematics |
| ISBN | : 9780521523363 |
A theory of the S-Matrix, starting from physically plausible assumptions and looking at the mathematical consequences.
| Author | : Fred Jegerlehner |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 433 |
| Release | : 2008 |
| Genre | : Science |
| ISBN | : 3540726330 |
This book reviews the present state of knowledge of the anomalous magnetic moment a=(g-2)/2 of the muon. The muon anomalous magnetic moment is one of the most precisely measured quantities in elementary particle physics and provides one of the most stringent tests of relativistic quantum field theory as a fundamental theoretical framework. It allows for an extremely precise check of the standard model of elementary particles and of its limitations.
| Author | : Bertfried Fauser |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 436 |
| Release | : 2009-06-02 |
| Genre | : Science |
| ISBN | : 376438736X |
The present volume emerged from the 3rd `Blaubeuren Workshop: Recent Developments in Quantum Field Theory', held in July 2007 at the Max Planck Institute of Mathematics in the Sciences in Leipzig/Germany. All of the contributions are committed to the idea of this workshop series: To bring together outstanding experts working in the field of mathematics and physics to discuss in an open atmosphere the fundamental questions at the frontier of theoretical physics.
| Author | : Liviu Nicolaescu |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 366 |
| Release | : 2011-12-02 |
| Genre | : Mathematics |
| ISBN | : 146141105X |
This self-contained treatment of Morse theory focuses on applications and is intended for a graduate course on differential or algebraic topology, and will also be of interest to researchers. This is the first textbook to include topics such as Morse-Smale flows, Floer homology, min-max theory, moment maps and equivariant cohomology, and complex Morse theory. The reader is expected to have some familiarity with cohomology theory and differential and integral calculus on smooth manifolds. Some features of the second edition include added applications, such as Morse theory and the curvature of knots, the cohomology of the moduli space of planar polygons, and the Duistermaat-Heckman formula. The second edition also includes a new chapter on Morse-Smale flows and Whitney stratifications, many new exercises, and various corrections from the first edition.
| Author | : Roland Glowinski |
| Publisher | : |
| Total Pages | : 472 |
| Release | : 2008-03-20 |
| Genre | : MATHEMATICS |
| ISBN | : 9781107096073 |
A thorough mathematical analysis of controllability problems with a detailed investigation of methods for solving them numerically.
| 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 | : Emily Clader |
| Publisher | : Springer |
| Total Pages | : 635 |
| Release | : 2019-04-08 |
| Genre | : Mathematics |
| ISBN | : 3319942204 |
This book collects various perspectives, contributed by both mathematicians and physicists, on the B-model and its role in mirror symmetry. Mirror symmetry is an active topic of research in both the mathematics and physics communities, but among mathematicians, the “A-model” half of the story remains much better-understood than the B-model. This book aims to address that imbalance. It begins with an overview of several methods by which mirrors have been constructed, and from there, gives a thorough account of the “BCOV” B-model theory from a physical perspective; this includes the appearance of such phenomena as the holomorphic anomaly equation and connections to number theory via modularity. Following a mathematical exposition of the subject of quantization, the remainder of the book is devoted to the B-model from a mathematician’s point-of-view, including such topics as polyvector fields and primitive forms, Givental’s ancestor potential, and integrable systems.
| 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.
