Download or read book Automatizing the Application of Mellin Barnes Representations for Feynman Integrals written by and published by . This book was released on 2007 with total page 10 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Mellin Barnes Integrals written by Ievgen Dubovyk and published by Springer Nature. This book was released on 2022-12-15 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Mellin Barnes Representations for Multiloop Feynman Integrals with Applications to 2 loop Electroweak Z Boson Studies written by Ievgen Dubovyk and published by . This book was released on 2019 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Mellin Barnes Representations of Feynman Diagrams Linear Systems of Differential Equations and Polynomial Solutions written by Mikhail Yu Kalmykov and published by . This book was released on 2012 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Analytic Tools for Feynman Integrals written by Vladimir A. Smirnov and published by Springer. This book was released on 2013-01-16 with total page 299 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Counting the Number of Master integrals for Sunrise type Feynman Diagrams Via Mellin Barnes Representation written by Mikhail Yu Kalmykov and published by . This book was released on 2017 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Non planar Feynman Diagrams and Mellin Barnes Representations with AMBRE 3 0 written by Ievgen Dubovyk and published by . This book was released on 2016 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Non planar Feynman Diagrams and Mellin Barnes Representations with AMBRE 3 0 written by I. Dubovyk and published by . This book was released on 2016 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Anti Differentiation and the Calculation of Feynman Amplitudes written by Johannes Blümlein and published by Springer Nature. This book was released on 2021-11-26 with total page 551 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume comprises review papers presented at the Conference on Antidifferentiation and the Calculation of Feynman Amplitudes, held in Zeuthen, Germany, in October 2020, and a few additional invited reviews. The book aims at comprehensive surveys and new innovative results of the analytic integration methods of Feynman integrals in quantum field theory. These methods are closely related to the field of special functions and their function spaces, the theory of differential equations and summation theory. Almost all of these algorithms have a strong basis in computer algebra. The solution of the corresponding problems are connected to the analytic management of large data in the range of Giga- to Terabytes. The methods are widely applicable to quite a series of other branches of mathematics and theoretical physics.
Download or read book Mellin Transform Method for Integral Evaluation written by George Fikioris and published by Springer Nature. This book was released on 2022-05-31 with total page 67 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces the Mellin-transform method for the exact calculation of one-dimensional definite integrals, and illustrates the application if this method to electromagnetics problems. Once the basics have been mastered, one quickly realizes that the method is extremely powerful, often yielding closed-form expressions very difficult to come up with other methods or to deduce from the usual tables of integrals. Yet, as opposed to other methods, the present method is very straightforward to apply; it usually requires laborious calculations, but little ingenuity. Two functions, the generalized hypergeometric function and the Meijer G-function, are very much related to the Mellin-transform method and arise frequently when the method is applied. Because these functions can be automatically handled by modern numerical routines, they are now much more useful than they were in the past. The Mellin-transform method and the two aforementioned functions are discussed first. Then the method is applied in three examples to obtain results, which, at least in the antenna/electromagnetics literature, are believed to be new. In the first example, a closed-form expression, as a generalized hypergeometric function, is obtained for the power radiated by a constant-current circular-loop antenna. The second example concerns the admittance of a 2-D slot antenna. In both these examples, the exact closed-form expressions are applied to improve upon existing formulas in standard antenna textbooks. In the third example, a very simple expression for an integral arising in recent, unpublished studies of unbounded, biaxially anisotropic media is derived. Additional examples are also briefly discussed.
Download or read book QCD Higher Order Effects and Search for New Physics written by Jian Wang and published by Springer. This book was released on 2015-10-28 with total page 153 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book mainly investigates the precision predictions on the signal of new physics at the Large Hadron Collider (LHC) in the perturbative Quantum Chromodynamics (QCD) scheme. The potential of the LHC to discover the signal of dark matter associated production with a photon is studied after including next-to-leading order QCD corrections. The factorization and resummation of t-channel top quark transverse momentum distribution in the standard model at both the Tevatron and the LHC with soft-collinear effective theory are presented. The potential of the early LHC to discover the signal of monotops is discussed. These examples illustrate the method of searching for new physics beyond what is known today with high precision.
Download or read book Deep Inelastic Scattering written by Masahiro Kuze and published by World Scientific. This book was released on 2007 with total page 996 pages. Available in PDF, EPUB and Kindle. Book excerpt: These proceedings present the most up-to-date status of deep inelastic scattering (DIS) physics. Topics such as structure function measurements and phenomenology, quantum chromodynamics (QCD) studies in DIS and photoproduction, spin physics and diffractive interactions are reviewed in detail, with emphasis on those studies that push the test of QCD and the Standard Model to the limits of their present range of validity, towards both the very high and the very low four-momentum transfers in leptonproton scattering.
Download or read book Renormalization and Galois Theories written by Frédéric Fauvet and published by European Mathematical Society. This book was released on 2009 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is the outcome of a CIRM Workshop on Renormalization and Galois Theories held in Luminy, France, in March 2006. The subject of this workshop was the interaction and relationship between four currently very active areas: renormalization in quantum field theory (QFT), differential Galois theory, noncommutative geometry, motives and Galois theory. The last decade has seen a burst of new techniques to cope with the various mathematical questions involved in QFT, with notably the development of a Hopf-algebraic approach and insights into the classes of numbers and special functions that systematically appear in the calculations of perturbative QFT (pQFT). The analysis of the ambiguities of resummation of the divergent series of pQFT, an old problem, has been renewed, using recent results on Gevrey asymptotics, generalized Borel summation, Stokes phenomenon and resurgent functions. The purpose of the present book is to highlight, in the context of renormalization, the convergence of these various themes, orchestrated by diverse Galois theories. It contains three lecture courses together with five research articles and will be useful to both researchers and graduate students in mathematics and physics.
Download or read book Scattering Amplitudes in Gauge Theories written by Johannes M. Henn and published by Springer. This book was released on 2014-02-07 with total page 206 pages. Available in PDF, EPUB and Kindle. Book excerpt: At the fundamental level, the interactions of elementary particles are described by quantum gauge field theory. The quantitative implications of these interactions are captured by scattering amplitudes, traditionally computed using Feynman diagrams. In the past decade tremendous progress has been made in our understanding of and computational abilities with regard to scattering amplitudes in gauge theories, going beyond the traditional textbook approach. These advances build upon on-shell methods that focus on the analytic structure of the amplitudes, as well as on their recently discovered hidden symmetries. In fact, when expressed in suitable variables the amplitudes are much simpler than anticipated and hidden patterns emerge. These modern methods are of increasing importance in phenomenological applications arising from the need for high-precision predictions for the experiments carried out at the Large Hadron Collider, as well as in foundational mathematical physics studies on the S-matrix in quantum field theory. Bridging the gap between introductory courses on quantum field theory and state-of-the-art research, these concise yet self-contained and course-tested lecture notes are well-suited for a one-semester graduate level course or as a self-study guide for anyone interested in fundamental aspects of quantum field theory and its applications. The numerous exercises and solutions included will help readers to embrace and apply the material present ed in the main text.
Download or read book Asymptotics and Mellin Barnes Integrals written by R. B. Paris and published by Cambridge University Press. This book was released on 2001-09-24 with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Evaluating Feynman Integrals written by Vladimir A. Smirnov and published by Springer. This book was released on 2005-02-28 with total page 251 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book The Analytic S Matrix written by R. J. Eden and published by Cambridge University Press. This book was released on 2002-04-30 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: A theory of the S-Matrix, starting from physically plausible assumptions and looking at the mathematical consequences.
