The Hopf algebra of IR divergences of Feynman graphs

Abstract: It is by now very well known that the structure of UV divergences Feynman Integrals, and their associated graphs, can be described elegantly in a Hopf algebra originally developed by Kreimer and Connes. Beyond UV divergences Feynman Integrals also suffer from IR, long-distance, divergences. I will present a new Hopf-algebraic formulation which allows to simultaneously treat both the IR and the UV. Remarkably in this framework the IR and UV counterterm maps are inverse to each other on the group of characters of the Hopf algebra.

commutative algebracombinatoricsoperator algebrasrings and algebras

Audience: researchers in the topic

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Algebraic and Combinatorial Perspectives in the Mathematical Sciences

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