Related papers: Symetries Galoisiennes et Renormalisation
We show how the Hopf algebra structure of renormalization discovered by Kreimer can be found in the Epstein-Glaser framework without using an analogue of the forest formula of Zimmermann.
In this note we discuss three interconnected problems about dynamics of Hamiltonian or, more generally, just smooth diffeomorphisms. The first two concern the existence and properties of the maps whose iterations approximate the identity…
We show that the logarithmic derivative of the gauge coupling on the hadronic mass and the cosmological constant term of a gauge theory are related to the gluon condensate of the hadron and the vacuum respectively. These relations are akin…
We study in this paper logarithmic derivatives associated to derivations on graded complete Lie algebra, as well as the existence of inverses. These logarithmic derivatives, when invertible, generalize the exp-log correspondence between a…
Given a Sylow $p$-subgroup $P$ of a symmetric group, we describe the action of its normalizer on $\mathrm{Irr}(P)$. To this end, we establish a one-to-one correspondence between the irreducible characters of $P$ and certain equivalence…
We relate the Belavin--Drinfeld cohomologies (twisted and untwisted) that have been introduced in the literature to study certain families of quantum groups and Lie bialgebras over a non algebraically closed field $\mathbb K$ of…
Every Hopf-Galois structure on a finite Galois extension $K/k$ where $G=Gal(K/k)$ corresponds uniquely to a regular subgroup $N\leq B=\operatorname{Perm}(G)$, normalized by $\lambda(G)\leq B$, in accordance with a theorem of Greither and…
In this paper the whole geometrical set-up giving a conformally invariant holographic projection of a diffeomorphism invariant bulk theory is clarified. By studying the renormalization group flow along null geodesic congruences a…
We discuss the relationship between geometry, the renormalization group (RG) and gravity. We begin by reviewing our recent work on crossover problems in field theory. By crossover we mean the interpolation between different representations…
A systematic procedure for performing holographic renormalization, which makes use of the Hamilton-Jacobi method, is proposed and applied to a bulk theory of gravity interacting with a scalar field and a U(1) gauge field in the Stueckelberg…
The symplectic derivation Lie algebras defined by Kontsevich are related to various geometric objects including moduli spaces of graphs and of Riemann surfaces, graph homologies, Hamiltonian vector fields, etc. Each of them and its…
In this paper we present a reformulation of the Galois correspondence theorem of Hopf Galois theory in terms of groups carrying farther the description of Greither and Pareigis. We prove that the class of Hopf Galois extensions for which…
We develop a real-analytic framework, called perplex analysis, in which the complex, split-complex, and dual numbers arise as members of a single four-parameter family of two-dimensional commutative real algebras. Within this unified…
We show that there exists a Galois correspondence between subalgebras of an H-comodule algebra A over a base ring R and generalised quotients of a Hopf algebra H if both A and H are flat Mittag--Leffler modules. We also provide new criteria…
If $\mathfrak{g} \subseteq \mathfrak{h}$ is an extension of Lie algebras over a field $k$ such that ${\rm dim}_k (\mathfrak{g}) = n$ and ${\rm dim}_k (\mathfrak{h}) = n + m$, then the Galois group ${\rm Gal} \, (\mathfrak{h}/\mathfrak{g})$…
Moving beyond the classical additive and multiplicative approaches, we present an "exponential" method for perturbative renormalization. Using Dyson's identity for Green's functions as well as the link between the Faa di Bruno Hopf algebra…
We investigate different Hopf algebras associated to Yang's solution of quantum Yang-Baxter equation. It is shown that for the precise definition of the algebra one needs the commutation relations for the deformed algebra of formal currents…
In this paper we introduce a space with some additional topologies using filter bases and renew the definition of Riemann surfaces of algebraic functions. We then present a Galois correspondence between these Riemann surfaces and their deck…
In a recent preprint, Brouder and Schmitt give a careful construction of a `renormalisation' Hopf algebra out of an arbitrary bialgebra. In this note, we point out that this is a special case of the construction of the cooperad of a…
We review Kreimer's construction of a Hopf algebra associated to the Feynman graphs of a perturbative quantum field theory.