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Free Rota-Baxter algebras and rooted trees
Kurusch Ebrahimi-Fard, Li Guo
A Rota-Baxter algebra, also known as a Baxter algebra, is an algebra with a linear operator satisfying a relation, called the Rota-Baxter relation, that generalizes the integration…
Hopf algebra approach to Feynman diagram calculations
Kurusch Ebrahimi-Fard, Dirk Kreimer
The Hopf algebra structure underlying Feynman diagrams which governs the process of renormalization in perturbative quantum field theory is reviewed. Recent progress is briefly sum…
Matrix Representation of Renormalization in Perturbative Quantum Field Theory
K. Ebrahimi-Fard, L. Guo
We formulate the Hopf algebraic approach of Connes and Kreimer to renormalization in perturbative quantum field theory using triangular matrix representation. We give a Rota-Baxter…
Combinatorics of renormalization as matrix calculus
K. Ebrahimi-Fard, J. M. Gracia-Bondia, L. Guo +1
We give a simple presentation of the combinatorics of renormalization in perturbative quantum field theory in terms of triangular matrices. The prescription, that may be of calcula…
Mixable Shuffles, Quasi-shuffles and Hopf Algebras
Kurusch Ebrahimi-Fard, Li Guo
The quasi-shuffle product and mixable shuffle product are both generalizations of the shuffle product and have both been studied quite extensively recently. We relate these two gen…
Rota-Baxter Algebras and Dendriform Algebras
Kurusch Ebrahimi-Fard, Li Guo
In this paper we study the adjoint functors between the category of Rota-Baxter algebras and the categories of dendriform dialgebras and trialgebras. In analogy to the well-known t…