Grassmannian Geometry of Scattering Amplitudes by Nima Arkani-Hamed (English) Ha

Description: Grassmannian Geometry of Scattering Amplitudes by Nima Arkani-Hamed, Jacob Bourjaily, Freddy Cachazo, Alexander Goncharov, Alexander Postnikov, Jaroslav Trnka An essential resource examining the ongoing revolution in our understanding of perturbative quantum field theory and its connection to Grassmannian geometry. This book outlines the foundations of this important new formulation, with a self-contained and authoritative analysis of its application to planar maximally supersymmetric Yang–Mills theory. FORMAT Hardcover LANGUAGE English CONDITION Brand New Publisher Description 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. Author Biography Nima Arkani-Hamed is Professor of Physics at the Institute for Advanced Study, Princeton. Jacob Bourjaily is Assistant Professor of Physics at the Niels Bohr International Academy and Discovery Center at the University of Copenhagen. Freddy Cachazo is the Gluskin Sheff Freeman Dyson Chair in Theoretical Physics at the Perimeter Institute for Theoretical Physics, Ontario. Alexander Goncharov is Professor of Mathematics at Yale University, Connecticut. Alexander Postnikov is Professor of Applied Mathematics and Algebraic Combinatorics at the Massachusetts Institute of Technology. Jaroslav Trnka is a Postdoctoral Researcher at California Institute of Technology. Table of Contents Acknowledgements; 1. Introduction; 2. Introduction to on-shell functions and diagrams; 3. Permutations and scattering amplitudes; 4. From on-shell diagrams to the Grassmannian; 5. Configurations of vectors and the positive Grassmannian; 6. Body configurations, graphs, and permutations; 7. The invariant top-form and the positroid stratification; 8. (Super) conformal and dual conformal invariance; 9. Positive diffeomorphisms and Yangian invariance; 10. The kinematical support of physical on-shell forms; 11. Homological identities among Yangian-invariants; 12. (Relatively) orienting canonical coordinate charts on positroids; 13. Classification of Yangian-invariants and their relations; 14. The Yang–Braxter relation and ABJM theories; 15. On-shell diagrams for theories with N Review This book describes the interesting mathematical structures behind scattering amplitudes, which have led to important simplifications for explicit computations. A must-read for people interested in this active and fast-moving field. Juan Maldacena, Institute for Advanced Study, PrincetonIn the continuing revolution in our understanding of scattering amplitudes in gauge theories, the emerging importance of Grassmannian geometry has been a considerable surprise. The consequences would have astonished the pioneers of quantum theory. This wonderful book, written by six of the fields leading pioneers, presents the new developments so clearly and eloquently that it will enable everyone with a basic knowledge of field theory to enter this hugely exciting branch of theoretical physics. Warmly recommended. Graham Farmelo, University of CambridgeThis book is the Diagrammar of the twenty-first century. Just as Gerard t Hooft and Martinus Veltman laid out in 1973 the then-new calculus of Feynman diagrams for scattering processes in non-abelian gauge theories, so now have Nima Arkani-Hamed and his co-authors set forth a new perspective on scattering amplitudes, which leads away from locality and unitarity toward other principles, and they have provided a detailed and elegantly illustrated how-to manual for the practitioner. Lance Dixon, Stanford University Promotional An essential guide to peturbative quantum field theory and its connection to Grassmannian geometry. Review Quote "This book is the Diagrammar of the twenty-first century. Just as Gerard t Hooft and Martinus Veltman laid out in 1973 the then-new calculus of Feynman diagrams for scattering processes in non-abelian gauge theories, so now have Nima Arkani-Hamed and his co-authors set forth a new perspective on scattering amplitudes, which leads away from locality and unitarity toward other principles, and they have provided a detailed and elegantly illustrated how-to manual for the practitioner." Lance Dixon, Stanford University Promotional "Headline" An essential guide to peturbative quantum field theory and its connection to Grassmannian geometry. Description for Bookstore An essential resource examining the ongoing revolution in our understanding of perturbative quantum field theory and its connection to Grassmannian geometry. This book outlines the foundations of this important new formulation, with a self-contained and authoritative analysis of its application to planar maximally supersymmetric Yang-Mills theory. Description for Library An essential resource examining the ongoing revolution in our understanding of perturbative quantum field theory and its connection to Grassmannian geometry. This book outlines the foundations of this important new formulation, with a self-contained and authoritative analysis of its application to planar maximally supersymmetric Yang-Mills theory. Details ISBN1107086582 Author Jaroslav Trnka Short Title GRASSMANNIAN GEOMETRY OF SCATT Publisher Cambridge University Press Language English ISBN-10 1107086582 ISBN-13 9781107086586 Media Book Format Hardcover Year 2016 Imprint Cambridge University Press Place of Publication Cambridge Country of Publication United Kingdom Publication Date 2016-05-05 Pages 201 Affiliation University of Copenhagen UK Release Date 2016-05-05 AU Release Date 2016-05-05 NZ Release Date 2016-05-05 Illustrations 8 Tables, black and white; 180 Halftones, unspecified; 12 Line drawings, unspecified Alternative 9781316091548 DEWEY 530.143 Audience Professional & Vocational We've got this At The Nile, if you're looking for it, we've got it. With fast shipping, low prices, friendly service and well over a million items - you're bound to find what you want, at a price you'll love! TheNile_Item_ID:168655528;

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