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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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G R A S S M A N N I A N G E O M E T RY O F S C AT T E R I N G A M P L I T U D E S
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. Nima Arkani-Hamed is Professor of Physics at the Institute for Advanced Study, Princeton, New Jersey, USA. Jacob Bourjaily is Assistant Professor of Physics at the Niels Bohr International Academy and Discovery Center at the University of Copenhagen, Copenhagen, Denmark. Freddy Cachazo is the Gluskin Sheff Freeman Dyson Chair in Theoretical Physics at the Perimeter Institute for Theoretical Physics, Waterloo, Ontario, Canada. Alexander Goncharov is Professor of Mathematics at Yale University, New Haven, Connecticut, USA. Alexander Postnikov is Professor of Applied Mathematics and Algebraic Combinatorics at the Massachusetts Institute of Technology, Cambridge, Massachusetts, USA. Jaroslav Trnka is Assistant Professor of Physics at the University of California, Davis, California, USA.
GRAS S M ANNI A N GE OME T RY OF
SCATTERING AMPLITUDES NIMA ARKANI-HAMED Institute for Advanced Study
JACO B BO U RJA ILY Niels Bohr Institute
F R E D DY C AC H A Z O Perimeter Institute
A L E X A N D E R G O N C H A ROV Yale University
A L E X A N D E R P O S T N I KOV Massachusetts Institute of Technology
JA RO S L AV T R N K A University of California, Davis
University Printing House, Cambridge CB2 8BS, United Kingdom Cambridge University Press is part of the University of Cambridge. It furthers the University’s mission by disseminating knowledge in the pursuit of education, learning and research at the highest international levels of excellence. www.cambridge.org Information on this title: www.cambridge.org/9781107086586 c Nima Arkani-Hamed, Jacob Bourjaily, Freddy Cachazo, Alexander Gonchar