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All Loop Scattering As A Counting Problem

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arxiv 2309.15913 v2 pith:V7FQ4AVD submitted 2023-09-27 hep-th

All Loop Scattering As A Counting Problem

classification hep-th
keywords scatteringamplitudescountingexpansionloopordersproblemtopological
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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This is the first in a series of papers presenting a new understanding of scattering amplitudes based on fundamentally combinatorial ideas in the kinematic space of the scattering data. We study the simplest theory of colored scalar particles with cubic interactions, at all loop orders and to all orders in the topological 't Hooft expansion. We find a novel formula for loop-integrated amplitudes, with no trace of the conventional sum over Feynman diagrams, but instead determined by a beautifully simple counting problem attached to any order of the topological expansion. These results represent a significant step forward in the decade-long quest to formulate the fundamental physics of the real world in a radically new language, where the rules of spacetime and quantum mechanics, as reflected in the principles of locality and unitarity, are seen to emerge from deeper mathematical structures.

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