Outlining a innovative reformulation of the principles of perturbative quantum box concept, this ebook is a self-contained and authoritative research of the applying of this new formula to the case of planar, maximally supersymmetric Yang-Mills concept. The booklet starts off by means of deriving connections among scattering amplitudes and Grassmannian geometry from first ideas earlier than introducing novel actual and mathematical principles in a scientific demeanour obtainable to either physicists and mathematicians. the primary gamers during this strategy are on-shell features that are heavily concerning sure sub-strata of Grassmannian manifolds known as positroids - when it comes to which the category of on-shell features and their kinfolk turns into combinatorially appear. this is often an important creation to the geometry and combinatorics of the positroid stratification of the Grassmannian and an excellent 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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