Outlining a progressive reformulation of the rules of perturbative quantum box concept, this publication is a self-contained and authoritative research of the appliance of this new formula to the case of planar, maximally supersymmetric Yang-Mills idea. The ebook starts via deriving connections among scattering amplitudes and Grassmannian geometry from first rules ahead of introducing novel actual and mathematical principles in a scientific demeanour obtainable to either physicists and mathematicians. the primary avid gamers during this procedure are on-shell capabilities that are heavily relating to definite sub-strata of Grassmannian manifolds known as positroids - by way of which the category of on-shell capabilities and their relatives turns into combinatorially occur. this is often a necessary creation to the geometry and combinatorics of the positroid stratification of the Grassmannian and a fantastic textual content for complicated scholars and researchers operating within the parts of box conception, excessive strength physics, and the wider fields of mathematical physics.

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