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Scattering Amplitudes In Gauge Theories

Author : Johannes M. Henn
ISBN : 9783642540226
Genre : Science
File Size : 42.62 MB
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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.
Category: Science

Scattering Amplitudes In Gauge Theory And Gravity

Author : Henriette Elvang
ISBN : 9781107069251
Genre : Science
File Size : 45.68 MB
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"This book grew out of a need to have a set of easily accessible notes that introduced the basic techniques used in modern research on scattering amplitudes. In addition to the key tools, such a review should collect some of the small results and intuitions the authors had acquired from their work in the eld and which had not reviously been exposed in the literature. As the authors quickly realized, such an introduction would bring the reader only part of the way towards some of the most exciting topics in the eld, so they decided to add a little extra" material. While doing so and this took quite a while the authors remained in full and complete denial about writing a book. It was only at the end of process that they faced their worst fears: the review was becoming a book. You now hold the result in your hands. Because the authors were not writing a book, they actually thoroughly enjoyed the work. Their hope is that you will enjoy it too and that you will nd it useful"--
Category: Science

Evolution Equations

Author : David Ellwood
ISBN : 9780821868614
Genre : Mathematics
File Size : 55.56 MB
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This volume is a collection of notes from lectures given at the 2008 Clay Mathematics Institute Summer School, held in Zürich, Switzerland. The lectures were designed for graduate students and mathematicians within five years of the Ph.D., and the main focus of the program was on recent progress in the theory of evolution equations. Such equations lie at the heart of many areas of mathematical physics and arise not only in situations with a manifest time evolution (such as linear and nonlinear wave and Schrödinger equations) but also in the high energy or semi-classical limits of elliptic problems. The three main courses focused primarily on microlocal analysis and spectral and scattering theory, the theory of the nonlinear Schrödinger and wave equations, and evolution problems in general relativity. These major topics were supplemented by several mini-courses reporting on the derivation of effective evolution equations from microscopic quantum dynamics; on wave maps with and without symmetries; on quantum N-body scattering, diffraction of waves, and symmetric spaces; and on nonlinear Schrödinger equations at critical regularity. Although highly detailed treatments of some of these topics are now available in the published literature, in this collection the reader can learn the fundamental ideas and tools with a minimum of technical machinery. Moreover, the treatment in this volume emphasizes common themes and techniques in the field, including exact and approximate conservation laws, energy methods, and positive commutator arguments. Titles in this series are co-published with the Clay Mathematics Institute (Cambridge, MA).
Category: Mathematics

Grassmannian Geometry Of Scattering Amplitudes

Author : Nima Arkani-Hamed
ISBN : 9781316571644
Genre : Science
File Size : 62.49 MB
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Outlining a revolutionary reformulation of the foundations of perturbative quantum field theory, this book is a self-contained and authoritative analysis of the application of this new formulation to the case of planar, maximally supersymmetric Yang–Mills theory. The book begins by deriving connections between scattering amplitudes and Grassmannian geometry from first principles before introducing novel physical and mathematical ideas in a systematic manner accessible to both physicists and mathematicians. The principle players in this process are on-shell functions which are closely related to certain sub-strata of Grassmannian manifolds called positroids - in terms of which the classification of on-shell functions and their relations becomes combinatorially manifest. This is an essential introduction to the geometry and combinatorics of the positroid stratification of the Grassmannian and an ideal text for advanced students and researchers working in the areas of field theory, high energy physics, and the broader fields of mathematical physics.
Category: Science

Introduction To Elementary Particles

Author : David Griffiths
ISBN : 9783527618477
Genre : Science
File Size : 79.15 MB
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This is the first quantitative treatment of elementary particle theory that is accessible to undergraduates. Using a lively, informal writing style, the author strikes a balance between quantitative rigor and intuitive understanding. The first chapter provides a detailed historical introduction to the subject. Subsequent chapters offer a consistent and modern presentation, covering the quark model, Feynman diagrams, quantum electrodynamics, and gauge theories. A clear introduction to the Feynman rules, using a simple model, helps readers learn the calculational techniques without the complications of spin. And an accessible treatment of QED shows how to evaluate tree-level diagrams. Contains an abundance of worked examples and many end-of-chapter problems.
Category: Science

Integrability Of Nonlinear Systems

Author : Yvette Kosmann-Schwarzbach
ISBN : 3540206302
Genre : Mathematics
File Size : 20.66 MB
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The lectures that comprise this volume constitute a comprehensive survey of the many and various aspects of integrable dynamical systems. The present edition is a streamlined, revised and updated version of a 1997 set of notes that was published as Lecture Notes in Physics, Volume 495. This volume will be complemented by a companion book dedicated to discrete integrable systems. Both volumes address primarily graduate students and nonspecialist researchers but will also benefit lecturers looking for suitable material for advanced courses and researchers interested in specific topics.
Category: Mathematics

Relativity And Scientific Computing

Author : Friedrich W. Hehl
ISBN : 9783642957321
Genre : Science
File Size : 41.80 MB
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For this set of lectures we assumed that the reader has a reasonable back ground in physics and some knowledge of general relativity, the modern theory of gravity in macrophysics, and cosmology. Computer methods are present ed by leading experts in the three main domains: in numerics, in computer algebra, and in visualization. The idea was that each of these subdisciplines is introduced by an extended set of main lectures and that each is conceived as being of comparable 'importance. Therefpre we believe that the book represents a good introduction into scientific I computing for any student who wants to specialize in relativity, gravitation, and/or astrophysics. We took great care to select lecturers who teach in a comprehensible way and who are, at the same time, at the research front of their respective field. In numerics we had the privilege of having a lecturer from the National Center for Supercomputing Applications (NCSA, Champaign, IL, USA) and some from other leading institutions of the world; visualization was taught by a visualization expert from Boeing; and in com puter algebra we took recourse to practitioners of different computer algebra systems as applied to classical general relativity up to quantum gravity and differential geometry.
Category: Science

Harmonic Superspace

Author : A. S. Galperin
ISBN : 1139430491
Genre : Science
File Size : 67.51 MB
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This is a pedagogical introduction to the harmonic superspace method in extended supersymmetry. Inspired by exciting developments in superstring theory, it provides a systematic treatment of the quantum field theories with N=2 and N=3 supersymmetry in harmonic superspace. The authors present the harmonic superspace approach as a means of providing an off-shell description of the N=2 supersymmetric theories, both at the classical and quantum levels. Furthermore, they show how it offers a unique way to construct an off-shell formulation of a theory with higher supersymmetry, namely the N=3 supersymmetric Yang-Mills theory. Harmonic Superspace makes manifest many remarkable geometric properties of the N=2 theories, for example, the one-to-one correspondence between N=2 supersymmetric matter, and hyper-Kähler and quaternionic manifolds. This book will be of interest to researchers and graduate students working in the areas of supersymmetric quantum field theory, string theory and complex geometries.
Category: Science

Science And Engineering Of Materials Si Edition

Author : Donald R. Askeland
ISBN : 9781305446335
Genre : Technology & Engineering
File Size : 80.45 MB
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Succeed in your materials science course with THE SCIENCE AND ENGINEERING OF MATERIALS, 7e. Filled with built-in study tools to help you master key concepts, this proven book will help you develop an understanding of the relationship between structure, processing, and properties of materials and will serve as a useful reference for future courses in manufacturing, materials, design, or materials selection. Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version.
Category: Technology & Engineering

Physics And Astrophysics Of Neutrinos

Author : Masataka Fukugita
ISBN : 9784431670292
Genre : Science
File Size : 54.2 MB
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Observations of neutrinos being emitted by the supernova SN1987A, star neutrinos, and atmospheric neutrinos have provided new insights into astronomy, as well as new unresolved phenomena such as the solar neutrino problem, spurring investigative studies among particle physicists and astrophysicists. One of the most important features of this book is its enumeration of a number of basic properties of neutrinos and their relationship to Grand Unified Theories, focusing on the origin of the neutrino's mass and the generation mixing of neutrinos. All the kamiokande results, detector performances, and complete references are included.
Category: Science