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Cover: 9781107086586 | Grassmannian Geometry of Scattering Amplitudes | Arkani-Hamed (u. a.)
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Grassmannian Geometry of Scattering Amplitudes
Buch von Nima Arkani-Hamed (u. a.)
Sprache: Englisch

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Beschreibung
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.
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.
Über den Autor
Nima Arkani-Hamed is Professor of Physics at the Institute for Advanced Study, Princeton.
Zusammenfassung
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.
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
Details
Erscheinungsjahr: 2016
Genre: Importe, Physik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
Inhalt: Gebunden
ISBN-13: 9781107086586
ISBN-10: 1107086582
Sprache: Englisch
Ausstattung / Beilage: HC gerader Rücken kaschiert
Einband: Gebunden
Autor: Arkani-Hamed, Nima
Bourjaily, Jacob
Cachazo, Freddy
Hersteller: Cambridge University Press
Maße: 250 x 175 x 16 mm
Von/Mit: Nima Arkani-Hamed (u. a.)
Erscheinungsdatum: 05.05.2016
Gewicht: 0,546 kg
Artikel-ID: 124035413
Über den Autor
Nima Arkani-Hamed is Professor of Physics at the Institute for Advanced Study, Princeton.
Zusammenfassung
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.
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
Details
Erscheinungsjahr: 2016
Genre: Importe, Physik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
Inhalt: Gebunden
ISBN-13: 9781107086586
ISBN-10: 1107086582
Sprache: Englisch
Ausstattung / Beilage: HC gerader Rücken kaschiert
Einband: Gebunden
Autor: Arkani-Hamed, Nima
Bourjaily, Jacob
Cachazo, Freddy
Hersteller: Cambridge University Press
Maße: 250 x 175 x 16 mm
Von/Mit: Nima Arkani-Hamed (u. a.)
Erscheinungsdatum: 05.05.2016
Gewicht: 0,546 kg
Artikel-ID: 124035413
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