# The Hopf algebra structure of the R∗-operation

@article{Beekveldt2020TheHA, title={The Hopf algebra structure of the R∗-operation}, author={Robert Beekveldt and Michael Borinsky and Franz Herzog}, journal={Journal of High Energy Physics}, year={2020}, volume={2020} }

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…

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