Outlining a innovative reformulation of the rules of perturbative quantum box conception, this booklet is a self-contained and authoritative research of the appliance of this new formula to the case of planar, maximally supersymmetric Yang-Mills concept. The e-book starts by means of deriving connections among scattering amplitudes and Grassmannian geometry from first ideas ahead of introducing novel actual and mathematical rules in a scientific demeanour obtainable to either physicists and mathematicians. the primary avid gamers during this approach are on-shell features that are heavily concerning convinced sub-strata of Grassmannian manifolds referred to as positroids - by way of which the class of on-shell capabilities and their family turns into combinatorially show up. this is often a vital creation to the geometry and combinatorics of the positroid stratification of the Grassmannian and an amazing textual content for complicated scholars and researchers operating within the parts of box conception, excessive power physics, and the wider fields of mathematical physics.
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