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Spitzer's Identity and the Algebraic Birkhoff Decomposition in pQFT
Kurusch Ebrahimi-Fard, Li Guo, Dirk Kreimer
In this article we continue to explore the notion of Rota-Baxter algebras in the context of the Hopf algebraic approach to renormalization theory in perturbative quantum field theo…
On Products and Duality of Binary, Quadratic, Regular Operads
Kurusch Ebrahimi-Fard, Li Guo
Since its introduction by Loday in 1995 with motivation from algebraic K-theory, dendriform dialgebras have been studied quite extensively with connections to several areas in math…
Integrable Renormalization II: the general case
Kurusch Ebrahimi-Fard, Li Guo, Dirk Kreimer
We extend the results we obtained in an earlier work. The cocommutative case of rooted ladder trees is generalized to a full Hopf algebra of (decorated) rooted trees. For Hopf alge…
Integrable Renormalization I: the Ladder Case
Kurusch Ebrahimi-Fard, Li Guo, Dirk Kreimer
In recent years a Hopf algebraic structure underlying the process of renormalization in quantum field theory was found. It led to a Birkhoff factorization for (regularized) Hopf al…