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- W2179497622 abstract "We study systems of combinatorial Dyson-Schwinger equations with an arbitrary number $N$ of coupling constants. The considered Hopf algebra of Feynman graphs is $mathbb{N}^N$-graded, and we wonder if the graded subalgebra generated by the solution is Hopf or not. We first introduce a family of pre-Lie algebras which we classify, dually providing systems generating a Hopf subalgebra, we also describe the associated groups, as extensions of groups of formal diffeomorphisms on several variables. We then consider systems coming from Feynman graphs of a Quantum Field Theory. We show that if the number $N$ of independent coupling constants is the number of interactions of the considered QFT, then the generated subalgebra is Hopf. For QED, $varphi^3$ and QCD, we also prove that this is the minimal value of $N$. All these examples are generalizations of the first family of Dyson-Schwinger systems in the one coupling constant case, called fundamental.We also give a generalization of the second family, called cyclic." @default.
- W2179497622 created "2016-06-24" @default.
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- W2179497622 date "2020-01-01" @default.
- W2179497622 modified "2023-09-25" @default.
- W2179497622 title "Mulitgraded Dyson-Schwinger systems" @default.
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