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Grassmannian Geometry of Scattering Amplitudes

BuchGebunden
206 Seiten
Englisch
Cambridge University Presserschienen am05.05.2016
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.mehr
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Produkt

KlappentextOutlining 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.
Details
ISBN/GTIN978-1-107-08658-6
ProduktartBuch
EinbandartGebunden
Erscheinungsjahr2016
Erscheinungsdatum05.05.2016
Seiten206 Seiten
SpracheEnglisch
MasseBreite 175 mm, Höhe 250 mm, Dicke 16 mm
Gewicht546 g
Artikel-Nr.37032738

Inhalt/Kritik

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