Outlining a innovative reformulation of the rules of perturbative quantum box concept, 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 thought. The e-book starts off by way of deriving connections among scattering amplitudes and Grassmannian geometry from first rules prior to introducing novel actual and mathematical rules in a scientific demeanour available to either physicists and mathematicians. the main gamers during this strategy are on-shell features that are heavily concerning yes sub-strata of Grassmannian manifolds known as positroids - by way of which the type of on-shell services and their family turns into combinatorially occur. this is often a necessary creation to the geometry and combinatorics of the positroid stratification of the Grassmannian and a terrific textual content for complicated scholars and researchers operating within the components of box conception, excessive power physics, and the wider fields of mathematical physics.
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