@MISC{Kreimer09threeétudes, author = {Dirk Kreimer and Zγ Zγ and Γi Γj}, title = {Three Études in QFT}, year = {2009} }

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Abstract

We review QFT from the algebraic structure of its perturbative expansion and point out three new results. Acknowledgments It is a pleasure to thank Spencer Bloch for questions which ultimately led to Theorem 3 below. The following is a write-up of an invited contribution to the International Congress for Mathematical Physics (Prague, 2009). Thanks are due to Pavel Exner and the other organizers. 1 Algebraic structure in local QFT In recent years we have collected a considerable amount of algebraic structure underlying the computational practice of quantum field theory, clarifying the mathematical foundations of these computations and coming to new insights in QFT, see [5, 1, 4, 6, 7] and references there for more detail and notation. In this section, we give a succinct summary. 1.1 Hopf and Lie algebras of graphs There is a Hopf and Lie algebras coming with 1PI Feynman graphs: