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arXiv · 2003.04301

The Hopf algebra structure of the $R^*$-operation

Robert Beekveldt·Michael Borinsky·Franz Herzog
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Abstract

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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Robert Beekveldt, Michael Borinsky, Franz Herzog. 2020-03-09. The Hopf algebra structure of the $R^*$-operation. https://doi.org/10.1007/jhep07(2020)061

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