201 citations · 2.4k across the 113 of their papers we have counts for
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A Lie theoretic approach to renormalization
K. Ebrahimi-Fard, J. M. Gracia-Bondia, F. Patras
Motivated by recent work of Connes and Marcolli, based on the Connes-Kreimer approach to renormalization, we augment the latter by a combinatorial, Lie algebraic point of view. Our…
On matrix differential equations in the Hopf algebra of renormalization
Kurusch Ebrahimi-Fard, Dominique Manchon
We establish Sakakibara's differential equations in a matrix setting for the counter term (respectively renormalized character) in Connes-Kreimer's Birkhoff decomposition in any co…
Generalized shuffles related to Nijenhuis and TD-algebras
K. Ebrahimi-Fard, P. Leroux
Shuffle and quasi-shuffle products are well-known in the mathematics literature. They are intimately related to Loday's dendriform algebras, and were extensively used to give expli…
Rota-Baxter Algebras in Renormalization of Perturbative Quantum Field Theory
Kurusch Ebrahimi-Fard, Li Guo
Recently, the theory of renormalization in perturbative quantum field theory underwent some exciting new developments. Kreimer discovered an organization of Feynman graphs into com…
Birkhoff type decompositions and the Baker-Campbell-Hausdorff recursion
K. Ebrahimi-Fard, L. Guo, D. Manchon
We describe a unification of several apparently unrelated factorizations arisen from quantum field theory, vertex operator algebras, combinatorics and numerical methods in differen…
Multiple zeta values and Rota--Baxter algebras
Kurusch Ebrahimi-Fard, Li Guo
We study multiple zeta values and their generalizations from the point of view of Rota--Baxter algebras. We obtain a general framework for this purpose and derive relations on mult…