Outlining a progressive reformulation of the principles of perturbative quantum box thought, 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 booklet starts off by means of deriving connections among scattering amplitudes and Grassmannian geometry from first rules earlier than introducing novel actual and mathematical rules in a scientific demeanour available to either physicists and mathematicians. the main gamers during this method are on-shell capabilities that are heavily regarding definite sub-strata of Grassmannian manifolds referred to as positroids - when it comes to which the type of on-shell capabilities and their kin turns into combinatorially occur. this can be an important 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 components of box conception, excessive power physics, and the wider fields of mathematical physics.
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