Scattering Amplitudes In Gauge Theories
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Scattering Amplitudes In Gauge Theories
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Author : Johannes M. Henn
language : en
Publisher: Springer
Release Date : 2014-02-07
Scattering Amplitudes In Gauge Theories written by Johannes M. Henn and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-02-07 with Science categories.
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.
Scattering Amplitudes In Gauge Theory And Gravity
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Author : Henriette Elvang
language : en
Publisher: Cambridge University Press
Release Date : 2015-02-05
Scattering Amplitudes In Gauge Theory And Gravity written by Henriette Elvang and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-02-05 with Science categories.
This book provides a comprehensive, pedagogical introduction to scattering amplitudes in gauge theory and gravity for graduate students.
Grassmannian Geometry Of Scattering Amplitudes
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Author : Nima Arkani-Hamed
language : en
Publisher: Cambridge University Press
Release Date : 2016-05-05
Grassmannian Geometry Of Scattering Amplitudes written by Nima Arkani-Hamed and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-05-05 with Mathematics categories.
An essential guide to peturbative quantum field theory and its connection to Grassmannian geometry.
Aspects Of Scattering Amplitudes And Moduli Space Localization
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Author : Sebastian Mizera
language : en
Publisher: Springer Nature
Release Date : 2020-09-23
Aspects Of Scattering Amplitudes And Moduli Space Localization written by Sebastian Mizera and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-09-23 with Science categories.
This thesis proposes a new perspective on scattering amplitudes in quantum field theories. Their standard formulation in terms of sums over Feynman diagrams is replaced by a computation of geometric invariants, called intersection numbers, on moduli spaces of Riemann surfaces. It therefore gives a physical interpretation of intersection numbers, which have been extensively studied in the mathematics literature in the context of generalized hypergeometric functions. This book explores physical consequences of this formulation, such as recursion relations, connections to geometry and string theory, as well as a phenomenon called moduli space localization. After reviewing necessary mathematical background, including topology of moduli spaces of Riemann spheres with punctures and its fundamental group, the definition and properties of intersection numbers are presented. A comprehensive list of applications and relations to other objects is given, including those to scattering amplitudes in open- and closed-string theories. The highlights of the thesis are the results regarding localization properties of intersection numbers in two opposite limits: in the low- and the high-energy expansion. In order to facilitate efficient computations of intersection numbers the author introduces recursion relations that exploit fibration properties of the moduli space. These are formulated in terms of so-called braid matrices that encode the information of how points braid around each other on the corresponding Riemann surface. Numerous application of this approach are presented for computation of scattering amplitudes in various gauge and gravity theories. This book comes with an extensive appendix that gives a pedagogical introduction to the topic of homologies with coefficients in a local system.
Introduction To Gauge Field Theory Revised Edition
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Author : D. Bailin
language : en
Publisher: CRC Press
Release Date : 1993-01-01
Introduction To Gauge Field Theory Revised Edition written by D. Bailin and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-01-01 with Science categories.
Introduction to Gauge Field Theory provides comprehensive coverage of modern relativistic quantum field theory, emphasizing the details of actual calculations rather than the phenomenology of the applications. Forming a foundation in the subject, the book assumes knowledge of relativistic quantum mechanics, but not of quantum field theory. The book is ideal for graduate students, advanced undergraduates, and researchers in the field of particle physics.
Scattering Amplitudes And Wilson Loops In Twistor Space
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Author : Mathew Richard Bullimore
language : en
Publisher: Springer
Release Date : 2013-10-30
Scattering Amplitudes And Wilson Loops In Twistor Space written by Mathew Richard Bullimore and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-10-30 with Science categories.
Scattering amplitudes are fundamental and rich observables in quantum field theory. Based on the observation that, for massless particles of spin-one or more, scattering amplitudes are much simpler than expected from traditional Feynman diagram techniques, the broad aim of this work is to understand and exploit this hidden structure. It uses methods from twistor theory to provide new insights into the correspondence between scattering amplitudes in supersymmetric Yang-Mills theory and null polygonal Wilson loops. By additionally exploiting the symmetries of the problem, the author succeeds in developing new ways of computing scattering amplitudes.
Classical Double Copy The New Connections In Gauge Theory And Gravity
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Author : Christopher White
language : en
Publisher: World Scientific
Release Date : 2024-04-22
Classical Double Copy The New Connections In Gauge Theory And Gravity written by Christopher White and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-04-22 with Science categories.
Our current understanding of nature is in terms of matter that is acted on by forces. There are four fundamental forces, of which three are described by so-called gauge theories, a type of quantum field theory. The fourth force, gravity, is best described by general relativity, and our traditional ways of thinking about gauge theories and gravity look completely different from each other.In recent years, an exciting new correspondence called the 'double copy' has emerged, which suggests that the above theories may be much more closely related than previously thought. Inspired by previous work in string theory, it originated in the study of how particles interact, but has since been generalised to show that many gravitational quantities can be simply obtained by recycling simpler gauge theory results. This has significant practical applications — such as new calculational tools for astrophysics — but is also of conceptual importance, in suggesting that our current ways of thinking about fundamental physics are hiding a vast underlying structure.This book reviews our current theories of fundamental physics, before describing in detail how the double copy was discovered, how it can be applied to different types of object in gauge or gravity theory, and what its current and future applications are. No prior knowledge of quantum field theory or string theory is assumed, such that the book will be of interest to a broad audience of physicists and mathematicians.
Modern Analytic Methods For Computing Scattering Amplitudes
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Author : Simone Zoia
language : en
Publisher: Springer Nature
Release Date : 2022-05-18
Modern Analytic Methods For Computing Scattering Amplitudes written by Simone Zoia and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-05-18 with Science categories.
This work presents some essential techniques that constitute the modern strategy for computing scattering amplitudes. It begins with an introductory chapter to fill the gap between a standard QFT course and the latest developments in the field. The author then tackles the main bottleneck: the computation of the loop Feynman integrals. The most efficient technique for their computation is the method of the differential equations. This is discussed in detail, with a particular focus on the mathematical aspects involved in the derivation of the differential equations and their solution. Ample space is devoted to the special functions arising from the differential equations, to their analytic properties, and to the mathematical techniques which allow us to handle them systematically. The thesis also addresses the application of these techniques to a cutting-edge problem of importance for the physics programme of the Large Hadron Collider: five-particle amplitudes at two-loop order. It presents the first analytic results for complete two-loop five-particle amplitudes, in supersymmetric theories and QCD. The techniques discussed here open the door to precision phenomenology for processes of phenomenological interest, such as three-photon, three-jet, and di-photon + jet production.
Combinatorial Aspects Of Scattering Amplitudes
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Author : Matteo Parisi
language : en
Publisher: Springer Nature
Release Date : 2023-12-11
Combinatorial Aspects Of Scattering Amplitudes written by Matteo Parisi and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-12-11 with Science categories.
This book is a significant contribution within and across High Energy Physics and Algebraic Combinatorics. It is at the forefront of the recent paradigm shift according to which physical observables emerge from geometry and combinatorics. It is the first book on the amplituhedron, which encodes the scattering amplitudes of N=4 Yang-Mills theory, a cousin of the theory of strong interactions of quarks and gluons. Amplituhedra are generalizations of polytopes inside the Grassmannian, and they build on the theory of total positivity and oriented matroids. This book unveils many new combinatorial structures of the amplituhedron and introduces a new important related object, the momentum amplituhedron. Moreover, the work pioneers the connection between amplituhedra, cluster algebras and tropical geometry. Combining extensive introductions with proofs and examples, it is a valuable resource for researchers investigating geometrical structures emerging from physics for some time to come.
Methods Of Contemporary Gauge Theory
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Author : Yuri Makeenko
language : en
Publisher: Cambridge University Press
Release Date : 2023-07-31
Methods Of Contemporary Gauge Theory written by Yuri Makeenko and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-07-31 with Science categories.