Numerical Integration Of Massive Two Loop Mellin Barnes Integrals In Minkowskian Regions

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Mellin-Barnes Integrals

Author : Ievgen Dubovyk
Publisher : Springer Nature
ISBN 13 : 3031142721
Total Pages : 296 pages
Book Rating : 4.0/5 (311 download)

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Book Synopsis Mellin-Barnes Integrals by : Ievgen Dubovyk

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.

Asymptotics and Mellin-Barnes Integrals

Author : R. B. Paris
Publisher : Cambridge University Press
ISBN 13 : 9781139430128
Total Pages : 452 pages
Book Rating : 4.4/5 (31 download)

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Book Synopsis Asymptotics and Mellin-Barnes Integrals by : R. B. Paris

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.

The Anomalous Magnetic Moment of the Muon

Author : Fred Jegerlehner
Publisher : Springer Science & Business Media
ISBN 13 : 3540726330
Total Pages : 433 pages
Book Rating : 4.5/5 (47 download)

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Book Synopsis The Anomalous Magnetic Moment of the Muon by : Fred Jegerlehner

Download or read book The Anomalous Magnetic Moment of the Muon written by Fred Jegerlehner and published by Springer Science & Business Media. This book was released on 2008 with total page 433 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

The Analytic S-Matrix

Author : R. J. Eden
Publisher : Cambridge University Press
ISBN 13 : 9780521523363
Total Pages : 300 pages
Book Rating : 4.5/5 (233 download)

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Book Synopsis The Analytic S-Matrix by : R. J. Eden

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.

Quantum Field Theory

Author : Bertfried Fauser
Publisher : Springer Science & Business Media
ISBN 13 : 376438736X
Total Pages : 436 pages
Book Rating : 4.7/5 (643 download)

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Book Synopsis Quantum Field Theory by : Bertfried Fauser

Download or read book Quantum Field Theory written by Bertfried Fauser and published by Springer Science & Business Media. This book was released on 2009-06-02 with total page 436 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

An Invitation to Morse Theory

Author : Liviu Nicolaescu
Publisher : Springer Science & Business Media
ISBN 13 : 146141105X
Total Pages : 366 pages
Book Rating : 4.4/5 (614 download)

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Book Synopsis An Invitation to Morse Theory by : Liviu Nicolaescu

Download or read book An Invitation to Morse Theory written by Liviu Nicolaescu and published by Springer Science & Business Media. This book was released on 2011-12-02 with total page 366 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Exact and Approximate Controllability for Distributed Parameter Systems

Author : Roland Glowinski
Publisher :
ISBN 13 : 9781107096073
Total Pages : 472 pages
Book Rating : 4.0/5 (96 download)

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Book Synopsis Exact and Approximate Controllability for Distributed Parameter Systems by : Roland Glowinski

Download or read book Exact and Approximate Controllability for Distributed Parameter Systems written by Roland Glowinski and published by . This book was released on 2008-03-20 with total page 472 pages. Available in PDF, EPUB and Kindle. Book excerpt: A thorough mathematical analysis of controllability problems with a detailed investigation of methods for solving them numerically.

Evaluating Feynman Integrals

Author : Vladimir A. Smirnov
Publisher : Springer
ISBN 13 : 3540447032
Total Pages : 251 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Evaluating Feynman Integrals by : Vladimir A. Smirnov

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.

B-Model Gromov-Witten Theory

Author : Emily Clader
Publisher : Springer
ISBN 13 : 3319942204
Total Pages : 635 pages
Book Rating : 4.3/5 (199 download)

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Book Synopsis B-Model Gromov-Witten Theory by : Emily Clader

Download or read book B-Model Gromov-Witten Theory written by Emily Clader and published by Springer. This book was released on 2019-04-08 with total page 635 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Feynman Integral Calculus

Author : Vladimir A. Smirnov
Publisher : Springer Science & Business Media
ISBN 13 : 3540306102
Total Pages : 288 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Feynman Integral Calculus by : Vladimir A. Smirnov

Download or read book Feynman Integral Calculus written by Vladimir A. Smirnov and published by Springer Science & Business Media. This book was released on 2006-08-02 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Spectral Theory of Infinite-Area Hyperbolic Surfaces

Author : David Borthwick
Publisher : Birkhäuser
ISBN 13 : 3319338773
Total Pages : 471 pages
Book Rating : 4.3/5 (193 download)

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Book Synopsis Spectral Theory of Infinite-Area Hyperbolic Surfaces by : David Borthwick

Download or read book Spectral Theory of Infinite-Area Hyperbolic Surfaces written by David Borthwick and published by Birkhäuser. This book was released on 2016-07-12 with total page 471 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text introduces geometric spectral theory in the context of infinite-area Riemann surfaces, providing a comprehensive account of the most recent developments in the field. For the second edition the context has been extended to general surfaces with hyperbolic ends, which provides a natural setting for development of the spectral theory while still keeping technical difficulties to a minimum. All of the material from the first edition is included and updated, and new sections have been added. Topics covered include an introduction to the geometry of hyperbolic surfaces, analysis of the resolvent of the Laplacian, scattering theory, resonances and scattering poles, the Selberg zeta function, the Poisson formula, distribution of resonances, the inverse scattering problem, Patterson-Sullivan theory, and the dynamical approach to the zeta function. The new sections cover the latest developments in the field, including the spectral gap, resonance asymptotics near the critical line, and sharp geometric constants for resonance bounds. A new chapter introduces recently developed techniques for resonance calculation that illuminate the existing results and conjectures on resonance distribution. The spectral theory of hyperbolic surfaces is a point of intersection for a great variety of areas, including quantum physics, discrete groups, differential geometry, number theory, complex analysis, and ergodic theory. This book will serve as a valuable resource for graduate students and researchers from these and other related fields. Review of the first edition: "The exposition is very clear and thorough, and essentially self-contained; the proofs are detailed...The book gathers together some material which is not always easily available in the literature...To conclude, the book is certainly at a level accessible to graduate students and researchers from a rather large range of fields. Clearly, the reader...would certainly benefit greatly from it." (Colin Guillarmou, Mathematical Reviews, Issue 2008 h)

Polylogarithms and Associated Functions

Author : Leonard Lewin
Publisher : North-Holland
ISBN 13 :
Total Pages : 386 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Polylogarithms and Associated Functions by : Leonard Lewin

Download or read book Polylogarithms and Associated Functions written by Leonard Lewin and published by North-Holland. This book was released on 1981 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Fundamentals of Speaker Recognition

Author : Homayoon Beigi
Publisher : Springer Science & Business Media
ISBN 13 : 0387775927
Total Pages : 984 pages
Book Rating : 4.3/5 (877 download)

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Book Synopsis Fundamentals of Speaker Recognition by : Homayoon Beigi

Download or read book Fundamentals of Speaker Recognition written by Homayoon Beigi and published by Springer Science & Business Media. This book was released on 2011-12-09 with total page 984 pages. Available in PDF, EPUB and Kindle. Book excerpt: An emerging technology, Speaker Recognition is becoming well-known for providing voice authentication over the telephone for helpdesks, call centres and other enterprise businesses for business process automation. "Fundamentals of Speaker Recognition" introduces Speaker Identification, Speaker Verification, Speaker (Audio Event) Classification, Speaker Detection, Speaker Tracking and more. The technical problems are rigorously defined, and a complete picture is made of the relevance of the discussed algorithms and their usage in building a comprehensive Speaker Recognition System. Designed as a textbook with examples and exercises at the end of each chapter, "Fundamentals of Speaker Recognition" is suitable for advanced-level students in computer science and engineering, concentrating on biometrics, speech recognition, pattern recognition, signal processing and, specifically, speaker recognition. It is also a valuable reference for developers of commercial technology and for speech scientists. Please click on the link under "Additional Information" to view supplemental information including the Table of Contents and Index.

Physics at the Terascale

Author : Ian Brock
Publisher : John Wiley & Sons
ISBN 13 : 3527634975
Total Pages : 437 pages
Book Rating : 4.5/5 (276 download)

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Book Synopsis Physics at the Terascale by : Ian Brock

Download or read book Physics at the Terascale written by Ian Brock and published by John Wiley & Sons. This book was released on 2011-05-04 with total page 437 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written by authors working at the forefront of research, this accessible treatment presents the current status of the field of collider-based particle physics at the highest energies available, as well as recent results and experimental techniques. It is clearly divided into three sections; The first covers the physics -- discussing the various aspects of the Standard Model as well as its extensions, explaining important experimental results and highlighting the expectations from the Large Hadron Collider (LHC). The second is dedicated to the involved technologies and detector concepts, and the third covers the important - but often neglected - topics of the organisation and financing of high-energy physics research. A useful resource for students and researchers from high-energy physics.

NIST Handbook of Mathematical Functions Hardback and CD-ROM

Author : Frank W. J. Olver
Publisher : Cambridge University Press
ISBN 13 : 0521192250
Total Pages : 968 pages
Book Rating : 4.5/5 (211 download)

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Book Synopsis NIST Handbook of Mathematical Functions Hardback and CD-ROM by : Frank W. J. Olver

Download or read book NIST Handbook of Mathematical Functions Hardback and CD-ROM written by Frank W. J. Olver and published by Cambridge University Press. This book was released on 2010-05-17 with total page 968 pages. Available in PDF, EPUB and Kindle. Book excerpt: The new standard reference on mathematical functions, replacing the classic but outdated handbook from Abramowitz and Stegun. Includes PDF version.

Elementary Particle Physics

Author : John Iliopoulos
Publisher : Oxford University Press
ISBN 13 : 0192658166
Total Pages : 522 pages
Book Rating : 4.1/5 (926 download)

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Book Synopsis Elementary Particle Physics by : John Iliopoulos

Download or read book Elementary Particle Physics written by John Iliopoulos and published by Oxford University Press. This book was released on 2021-10-25 with total page 522 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since the development of natural philosophy in Ancient Greece, scientists have been concerned with determining the nature of matter's smallest constituents and the interactions among them. This textbook examines the question of the microscopic composition of matter through an accessible introduction to what is now called 'The Physics of Elementary Particles'. In the last few decades, elementary particle physics has undergone a period of transition, culminating in the formulation of a new theoretical scheme, known as 'The Standard Model', which has profoundly changed our understanding of nature's fundamental forces. Rooted in the experimental tradition, this new vision is based on geometry and sees the composition of matter in terms of its accordance with certain geometrical principles. This textbook presents and explains this modern viewpoint to a readership of well-motivated undergraduate students, by guiding the reader from the basics to the more advanced concepts of Gauge Symmetry, Quantum Field Theory and the phenomenon of spontaneous symmetry breaking through concrete physical examples. This engaging introduction to the theoretical advances and experimental discoveries of the last decades makes this fascinating subject accessible to undergraduate students and aims at motivating them to study it further.

Number Theory

Author : Benjamin Fine
Publisher : Birkhäuser
ISBN 13 : 3319438751
Total Pages : 423 pages
Book Rating : 4.3/5 (194 download)

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Book Synopsis Number Theory by : Benjamin Fine

Download or read book Number Theory written by Benjamin Fine and published by Birkhäuser. This book was released on 2016-09-19 with total page 423 pages. Available in PDF, EPUB and Kindle. Book excerpt: Now in its second edition, this textbook provides an introduction and overview of number theory based on the density and properties of the prime numbers. This unique approach offers both a firm background in the standard material of number theory, as well as an overview of the entire discipline. All of the essential topics are covered, such as the fundamental theorem of arithmetic, theory of congruences, quadratic reciprocity, arithmetic functions, and the distribution of primes. New in this edition are coverage of p-adic numbers, Hensel's lemma, multiple zeta-values, and elliptic curve methods in primality testing. Key topics and features include: A solid introduction to analytic number theory, including full proofs of Dirichlet's Theorem and the Prime Number Theorem Concise treatment of algebraic number theory, including a complete presentation of primes, prime factorizations in algebraic number fields, and unique factorization of ideals Discussion of the AKS algorithm, which shows that primality testing is one of polynomial time, a topic not usually included in such texts Many interesting ancillary topics, such as primality testing and cryptography, Fermat and Mersenne numbers, and Carmichael numbers The user-friendly style, historical context, and wide range of exercises that range from simple to quite difficult (with solutions and hints provided for select exercises) make Number Theory: An Introduction via the Density of Primes ideal for both self-study and classroom use. Intended for upper level undergraduates and beginning graduates, the only prerequisites are a basic knowledge of calculus, multivariable calculus, and some linear algebra. All necessary concepts from abstract algebra and complex analysis are introduced where needed.