Algebra of graphs for scattering dynamics

Abstract: Feynman diagrams are an iconic instance of diagrammatic tools in theoretical physics, which were developed for describing quantum scattering dynamics of particles in quantum field theory. With a small modification to diagrammatic rules, the Feynman diagrams can be repurposed to describe classical scattering dynamics, where rooted tree graphs are given a special role of computing the impulse (momentum change from scattering). I will explain how repackaging the classical scattering dynamics as a symmetry transformation (symplectic transformation) leads to the Poisson algebra of directed tree graphs, the Magnus series, and the Hopf algebra of graphs by Calaque, Ebrahimi-Fard, and Manchon. This talk is based on arXiv:2410.22988 [hep-th], a work in collaboration with Joon-Hwi Kim, Sungsoo Kim, and Sangmin Lee.

machine learningcommutative algebraalgebraic geometryalgebraic topologycombinatoricscategory theoryoperator algebrasrings and algebrasrepresentation theory

Audience: researchers in the topic

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Algebraic and Combinatorial Perspectives in the Mathematical Sciences

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