Grassmannian Geometry of Scattering Amplitudes 1st Edition by Nima Arkani Hamed,Jacob Bourjaily,Freddy Cachazo,Alexander Goncharov,Alexander Postnikov,Jaroslav Trnka ISBN 1107086582 978-1107086586

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Product details:

ISBN 10: 1107086582

ISBN 13: 978-1107086586 

Author: Nima Arkani-Hamed, Jacob Bourjaily, Freddy Cachazo, Alexander Goncharov, Alexander Postnikov, Jaroslav Trnka

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.

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. Boundary 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 configurations

13. Classification of Yangian-invariants and their relations

14. The Yang–Baxter 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

19. References

20. Index

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Tags: Nima Arkani Hamed, Jacob Bourjaily, Freddy Cachazo, Alexander Goncharov, Alexander Postnikov, Jaroslav Trnka, Grassmannian Geometry, of Scattering Amplitudes