Related papers: Renormalization and Mellin transforms
This article aims to give a short introduction into Hopf-algebraic aspects of renormalization, enjoying growing attention for more than a decade by now. As most available literature is concerned with the minimal subtraction scheme, we like…
This masters thesis reviews the algebraic formulation of renormalization using Hopf algebras as pioneered by Dirk Kreimer and applies it to a toy model of quantum field theory given through iterated insertions of a single primitive…
It was recently shown that the renormalization of quantum field theory is organized by the Hopf algebra of decorated rooted trees, whose coproduct identifies the divergences requiring subtraction and whose antipode achieves this. We…
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 algebra characters, i.e. for Feynman rules. In this work we…
In this paper we are going to find a rooted tree representation from universal Hopf algebra of renormalization (in Connes-Marcolli's approach in the study of renormalizable Quantum Field Theories under the scheme minimal subtraction in…
We consider the structure of renormalizable quantum field theories from the viewpoint of their underlying Hopf algebra structure. We review how to use this Hopf algebra and the ensuing Hochschild cohomology to derive non-perturbative…
This paper gives a complete selfcontained proof of our result announced in hep-th/9909126 showing that renormalization in quantum field theory is a special instance of a general mathematical procedure of extraction of finite values based on…
It is well known that the mathematical structure underlying renormalization in perturbative quantum field theory is based on a Hopf algebra of Feynman diagrams. A precondition for this is locality of the field theory. Consequently, one…
This paper is devoted to the study of renormalization of the quartic melonic tensor model in dimension (=rank) five. We review the perturbative renormalization and the computation of the one loop beta function, confirming the asymptotic…
Connes and Kreimer have discovered a Hopf algebra structure behind renormalization of Feynman integrals. We generalize the Hopf algebra to the case of ribbon graphs, i.e. to the case of theories with matrix fields. The Hopf algebra is…
The Hopf algebra structure underlying Feynman diagrams which governs the process of renormalization in perturbative quantum field theory is reviewed. Recent progress is briefly summarized with an emphasis on further directions of research.
We define in this paper several Hopf algebras describing the combinatorics of the so-called multi-scale renormalization in quantum field theory. After a brief recall of the main mathematical features of multi-scale renormalization, we…
The Hopf algebra and the Rota-Baxter algebra are the two algebraic structures underlying the algebraic approach of Connes and Kreimer to renormalization of perturbative quantum field theory. In particular the Hopf algebra of rooted trees…
We analyse the Dirichlet convolution ring of arithmetic number theoretic functions. It turns out to fail to be a Hopf algebra on the diagonal, due to the lack of complete multiplicativity of the product and coproduct. A related Hopf algebra…
We briefly review the Hopf algebra structure arising in the renormalization of quantum field theories. We construct the Hopf algebra explicitly for a simple toy model and show how renormalization is achieved for this particular model.
Continuing work begin in arXiv:1910.12609, we interpret the Hurewicz homomorphism for Baker and Richter's noncommutative complex cobordism spectrum $M\xi$ in terms of characteristic numbers (indexed by quasi-symmetric functions) for…
In 1999, A. Connes and D. Kreimer have discovered the Hopf algebra structure on the Feynman graphs of scalar field theory. They have found that the renormalization can be interpreted as a solving of some Riemann -- Hilbert problem. In this…
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 algebra characters with target space of Rota-Baxter type, the…
In this paper we describe the Hopf algebras on planar binary trees used to renormalize the Feynman propagators of quantum electrodynamics, and the coaction which describes the renormalization procedure. Both structures are related to some…
We show how the Hopf algebra of rooted trees encodes the combinatorics of Epstein-Glaser renormalization and coordinate space renormalization in general. In particular we prove that the Epstein-Glaser time-ordered products can be obtained…