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Grassmannian Geometry of Scattering Amplitudes

$58.00 ( ) USD

  • Date Published: April 2016
  • availability: This ISBN is for an eBook version which is distributed on our behalf by a third party.
  • format: Adobe eBook Reader
  • isbn: 9781316572962

$ 58.00 USD ( )
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About the Authors
  • 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.

    • Features an authoritative introduction to the foundations of a rapidly growing subject by leading experts in the field
    • Provides a single, comprehensive reference for the physical and mathematical tools in the case of planar SYM
    • Includes the downloadable Mathematica package, 'positroids', which is a comprehensive set of computational tools for studying the examples described in this book
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    Reviews & endorsements

    "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, Princeton

    "In 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 field's 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 Cambridge

    "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

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    Product details

    • Date Published: April 2016
    • format: Adobe eBook Reader
    • isbn: 9781316572962
    • contains: 192 b/w illus. 8 tables
    • availability: This ISBN is for an eBook version which is distributed on our behalf by a third party.
  • Table of Contents

    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<4 supersymmetries
    16. Dual graphs and cluster algebras
    17. On-shell representations of scattering amplitudes
    18. Outlook

  • Authors

    Nima Arkani-Hamed, Institute for Advanced Study, Princeton, New Jersey

    Jacob Bourjaily, University of Copenhagen

    Freddy Cachazo, Perimeter Institute for Theoretical Physics, Ontario

    Alexander Goncharov, Yale University, Connecticut

    Alexander Postnikov, Massachusetts Institute of Technology

    Jaroslav Trnka, California Institute of Technology

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