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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…
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…
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…
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…