Grassmannian Geometry of Scattering Amplitudes

5c78e5e016274.jpg Author Alexander Goncharov, Alexander Postnikov, Freddy Cachazo, Jacob Bourjaily, and Nima Arkani-Hamed
Isbn 9781107086586
File size 8MB
Year 2016
Pages 201
Language English
File format PDF
Category Physics

Book Description:

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.

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