Related papers: Renormalization: a quasi-shuffle approach
In recent years, The BPHZ algorithm for renormalization in quantum field theory has been interpreted, after dimensional regularization, as the Birkhoff-(Rota-Baxter) decomposition (BRB) of characters on the Hopf algebra of Feynmann graphs,…
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…
The Hopf algebra of renormalization in quantum field theory is described at a general level. The products of fields at a point are assumed to form a bialgebra B and renormalization endows T(T(B)^+), the double tensor algebra of B, with the…
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 anti-homomorphism from general regularized functionals on…
This paper gives a review of Connes-Kreimer formulation of perturbative renormalization in Quantum Field Theory. We begin with the derivation of the Feynman calculus, the Hopf algebra structure on Feynman diagrams and we show the natural…
Recently, the theory of renormalization in perturbative quantum field theory underwent some exciting new developments. Kreimer discovered an organization of Feynman graphs into combinatorial Hopf algebras. The process of renormalization is…
The objective of this work is to compare several approaches to the process of renormalisation in the context of rough differential equations using the substitution bialgebra on rooted trees known from backward error analysis of $B$-series.…
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…
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…
We construct a Hopf algebra structure on the space of specified Feynman graphs of a quantum field theory. We introduce a convolution product and a semigroup of characters of this Hopf algebra with values in some suitable commutative algebra…
We showed in part I (hep-th/9912092) that the Hopf algebra ${\cal H}$ of Feynman graphs in a given QFT is the algebra of coordinates on a complex infinite dimensional Lie group $G$ and that the renormalized theory is obtained from the…
In this work, we provide a method to obtain the renormalised measure in quantum field theory directly from the renormalisation of the expansion of the original measure. Our approach is based on BPHZ renormalisation via multi-indices, a…
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…
The structure of the Connes-Kreimer renormalization Hopf algebra is studied for gauge theories, with particular emphasis on the BRST-formalism. We work in the explicit example of quantum chromodynamics, the physical theory of quarks and…
We study renormalization in a kinetic scheme using the Hopf algebraic framework, first summarizing and recovering known results in this setting. Then we give a direct combinatorial description of renormalized amplitudes in terms of Mellin…
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 observe that the Connes--Kreimer Hopf-algebraic approach to perturbative renormalisation works not just for Hopf algebras but more generally for filtered bialgebras $B$ with the property that $B_0$ is spanned by group-like elements (e.g.…
We study the structure of renormalization Hopf algebras of gauge theories. We identify certain Hopf subalgebras in them, whose character groups are semidirect products of invertible formal power series with formal diffeomorphisms. This can…
As a natural basis of the Hopf algebra of quasisymmetric functions, monomial quasisymmetric functions are formal power series defined from compositions. The same definition applies to left weak compositions, while leads to divergence for…
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 theory. We show in very simple algebraic terms that the…