Mathematics

In this talk we introduce the so-called exponential renormalization method, developed in the context of the Connes-Kreimer Hopf algebra of Feynman graphs. Using Dyson\'s identity for Green\'s functions as well as the link between the Faà di Bruno Hopf algebra and Hopf algebras of Feynman graphs, its relation to the composition of formal power series is analyzed. This leads to the introduction of the notion of counterfactors and order n bare coupling constants. Eventually we analyze the role of the Rota-Baxter property for renormalization scheme maps. \r\n\r\nKEF, F. Patras: \"Exponential renormalization\", Ann. Henri Poincaré 11 (2010), 943-971; \"Exponential Renormalization II: Bogoliubov\'s R-operation and momentum subtraction schemes\", J. Math. Phys. 53, 083505 (2012).\r\n\r\n