Related papers: Exponential renormalization
In a recent work a modified BPHZ scheme has been introduced and applied to one-loop Feynman graphs in non-commutative phi^4-theory. In the present paper, we first review the BPHZ method and then we apply the modified BPHZ scheme as well as…
In a perturbative approach Einstein-Hilbert gravity is quantized about a flat background. In order to render the model power counting renormalizable, higher order curvature terms are added to the action. They serve as Pauli-Villars type…
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…
A new proof of perturbative renormalizability and infrared finiteness for a scalar massless theory is obtained from a formulation of renormalized field theory based on the Wilson renormalization group. The loop expansion of the renormalized…
We show how to use the Hopf algebra structure of quantum field theory to derive nonperturbative results for the short-distance singular sector of a renormalizable quantum field theory in a simple but generic example. We discuss renormalized…
Subdivergences constitute a major obstacle to the evaluation of Feynman integrals and an expression in terms of finite quantities can be a considerable advantage for both analytic and numeric calculations. We report on our implementation of…
We present a self-consistent approach for computing the correlated quasiparticle spectrum of charged excitations in iterative $\mathcal{O}[N^5]$ computational time. This is based on the auxiliary second-order Green's function approach [O.…
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.…
Central in the Hopf algebra approach to the renormalization of perturbative quantum field theory of Connes and Kreimer is their Algebraic Birkhoff Decomposition. In this tutorial article, we introduce their decomposition and prove it by the…
In order to understand the dynamical mechanism of the friction phenomena, we heavily rely on the numerical analysis using various methods: molecular dynamics, Langevin equation, lattice Boltzmann method, Monte Carlo, e.t.c.. We propose a…
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…
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 establish Sakakibara's differential equations in a matrix setting for the counter term (respectively renormalized character) in Connes-Kreimer's Birkhoff decomposition in any connected graded Hopf algebra, thus including Feynman rules in…
We consider the combinatorial Dyson-Schwinger equation X=B^+(P(X)) in the non-commutative Connes-KreimerHopf algebra of planar rooted trees H, where B^+ is the operator of grafting on a root, and P a formal series. The unique solution X of…
We show that general cutoff scalar field theories in four dimensions are perturbatively renormalizable through the use of diagrammatic techniques and an adapted BPH renormalization method. Weinberg's convergence theorem is used to show that…
We give a systematic description of a canonical renormalisation procedure of stochastic PDEs containing nonlinearities involving generalised functions. This theory is based on the construction of a new class of regularity structures which…
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…
We construct a manifest gauge invariant renormalization framework by first introducing a perturbative BRST Feynman graph complex and then combining it with Connes--Kreimer renormalization theory: To this end, we first formalize the…
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…
In this article, we define a doubling procedure for the bialgebra of specified Feynman graphs introduced in a previous paper \cite {DMB}. This is the vector space generated by the pairs $(\bar \Gamma, \bar \gamma)$ where $\bar \Gamma$ is a…