Grassmannian Geometry of Scattering Amplitudes

ISBN-13: 9781107086586 / Angielski / Twarda / 2016 / 201 str.

Nima Arkani-Hamed; Jacob Bourjaily; Freddy Cachazo

Opis

An essential guide to peturbative quantum field theory and its connection to Grassmannian geometry.

Recenzje

'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

Spis treści

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.