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Beekveldt, Robert; Borinsky, Michael; Herzog, Franz
The journal of high energy physics, 07/2020, Letnik: 2020, Številka: 7Journal Article
A bstract We give a Hopf-algebraic formulation of the R ∗ -operation, which is a canonical way to render UV and IR divergent Euclidean Feynman diagrams finite. Our analysis uncovers a close connection to Brown’s Hopf algebra of motic graphs. Using this connection we are able to provide a verbose proof of the long observed ‘commutativity’ of UV and IR subtractions. We also give a new duality between UV and IR counterterms, which, entirely algebraic in nature, is formulated as an inverse relation on the group of characters of the Hopf algebra of log-divergent scaleless Feynman graphs. Many explicit examples of calculations with applications to infrared rearrangement are given.
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