Related papers: Renormalising Feynman diagrams with multi-indices
We propose a numerical method for resummation of perturbative series, which is based on the stochastic perturbative solution of Schwinger-Dyson equations. The method stochastically estimates the coefficients of perturbative series, and…
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.…
Definition of Feynman integrals as solutions of some well defined systems of differential equations is proposed. This definition is equivalent to usual one but needs no regularization and application of $R$-operation. It is argued that…
We construct an explicit Hopf algebra isomorphism from the algebra of heap-ordered trees to that of quasi-symmetric functions, generated by formal permutations, which is a lift of the natural projection of the Connes-Kreimer algebra of…
An ill-defined integral equation for modeling the mass-spectrum of mesons is regulated with an additional but unphysical parameter. This parameter dependance is removed by renormalization. Illustrative graphical examples are given.
Hairer's regularity structures transformed the solution theory of singular stochastic partial differential equations. The notions of positive and negative renormalisation are central and the intricate interplay between these two…
An algorithm for the reduction of one-loop n-point tensor integrals to basic integrals is proposed. We transform tensor integrals to scalar integrals with shifted dimension and reduce these by recurrence relations to integrals in generic…
The quantum-field renormalization group method is one of the most efficient and powerful tools for studying critical and scaling phenomena in interacting many-particle systems. The multiloop Feynman diagrams underpin the specific…
We review here the parametric representation of Feynman amplitudes of renormalizable non-commutative quantum field models.
We construct renormalised models of regularity structures by using a recursive formulation for the structure group and for the renormalisation group. This construction covers all the examples of singular SPDEs which have been treated so far…
I review various aspects of Feynman integrals, regularization and renormalization. Following Bloch, I focus on a linear algebraic approach to the Feynman rules, and I try to bring together several renormalization methods found in the…
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…
This article aims at advancing the recently introduced exponential method for renormalisation in perturbative quantum field theory. It is shown that this new procedure provides a meaningful recursive scheme in the context of the algebraic…
We discuss how basic notions of graph theory and associated graph polynomials define questions for algebraic geometry, with an emphasis given to an analysis of the structure of Feynman rules as determined by those graph polynomials as well…
Within finite temperature field theory, we show that truncated non-perturbative self-consistent Dyson resummation schemes can be renormalized with local vacuum counterterms. For this the theory has to be renormalizable in the usual sense…
Feynman diagrams are the foremost tool in the perturbative study of quantum field theory. In gauge theories, the full potential of this tool is revealed when it is combined with the Slavanov-Taylor identities associated with the local gauge…
We introduce a general class of combinatorial objects, which we call \emph{multi-complexes}, which simultaneously generalizes graphs, multigraphs, hypergraphs and simplicial and delta complexes. We introduce a natural algebra of…
We consider three a priori totally different setups for Hopf algebras from number theory, mathematical physics and algebraic topology. These are the Hopf algebra of Goncharov for multiple zeta values, that of Connes-Kreimer for…
In a recent paper by the author (Chen in JHEP 02:115, 2020), the reduction of Feynman integrals in the parametric representation was considered. Tensor integrals were directly parametrized by using a generator method. The resulting…
We construct a three-parameter deformation of the Hopf algebra $\LDIAG$. This is the algebra that appears in an expansion in terms of Feynman-like diagrams of the {\em product formula} in a simplified version of Quantum Field Theory. This…