Related papers: Renormalization: a quasi-shuffle approach
We propose a treatment of $\gamma^5$ in dimensional regularization which is based on an algebraically consistent extension of the Breitenlohner-Maison-'t Hooft-Veltman (BMHV) scheme; we define the corresponding minimal renormalization…
We provide an algebraic framework to describe renormalization in regularity structures based on multi-indices for a large class of semi-linear stochastic PDEs. This framework is ``top-down", in the sense that we postulate the form of the…
In this paper, we develop a wave function renormalization scheme for models of non-relativistic quantum particles interacting with a quantized relativistic field, in the Hamiltonian formalism of quantum field theory. We construct the…
This paper argues that the ideas underlying the renormalization group technique used to characterize phase transitions in condensed matter systems could be useful for distinguishing computational complexity classes. The paper presents a…
It is shown that the renormalization group (RG) method for global analysis can be formulated in the context of the classical theory of envelopes: Several examples from partial differential equations are analyzed. The amplitude equations…
Quantum field theories require a cutoff to regulate divergences that result from local interactions, and yet physical results can not depend on the value of this cutoff. The renormalization group employs a transformation that changes the…
We study the renormalization group equations following from the Hopf algebra of graphs. Vertex functions are treated as vectors in dual to the Hopf algebra space. The RG equations on such vertex functions are equivalent to RG equations on…
We present the Hopf algebra of renormalization and introduce the renormalization group equation in this framework. Some linear Schwinger--Dyson equations are studied, and exact solutions are presented. Then we study the Schwinger--Dyson…
These are the notes of five lectures given at the Summer School {\em Geometric and Topological Methods for Quantum Field Theory}, held in Villa de Leyva (Colombia), July 2--20, 2007. The lectures are meant for graduate or almost graduate…
We review the techniques used to renormalize quantum field theories at several loop orders. This includes the techniques to systematically extract the infinities in a Feynman integral and the implementation of the algorithm within computer…
We present a systematic implementation of differential renormalization to all orders in perturbation theory. The method is applied to individual Feynamn graphs written in coordinate space. After isolating every singularity. which appears in…
We give a holographic explanation how the renormalization group approach to singular perturbations in non-linear differential equations proposed by Chen, Goldenfeld and Oono is indeed equivalent to a renormalization group method in quantum…
The search for elliptic quantum groups leads to a modified quantum Yang-Baxter relation and to a special class of quasi-triangular quasi Hopf algebras. This paper calculates deformations of standard quantum groups (with or without spectral…
The study of the Berezinskii-Kosterlitz-Thouless transition in two-dimensional $|\varphi|^4$ models can be performed in several representations, and the amplitude-phase (AP) Madelung parametrization is a natural way to study the…
We explore the relation between the Hopf algebra associated to the renormalization of QFT and the Hopf algebra associated to the NCG computations of transverse index theory for foliations.
We apply a soft version of the BPHZ subtraction scheme to the computation of two-loop corrections from an Abelian Chern-Simons field coupled to (massive) scalar matter with a $\lambda(\Phi^\dag\Phi)^2$ and $\nu(\Phi^\dag\Phi)^3$…
In this short survey we present the appearance of some combinatorial notions in quantum field theory. We first focus on topological graph polynomials (the Tutte polynomial and its multivariate version) and their relation with the parametric…
Our goal in this paper is to present a generalization of the spectral zeta regularization for general Feynman amplitudes. Our method uses complex powers of elliptic operators but involves several complex parameters in the spirit of the…
We investigate combinatorial and algebraic aspects of the interplay between renormalization and monodromies for Feynman amplitudes. We clarify how extraction of subgraphs from a Feynman graph interacts with putting edges onshell or with…
The exact or Wilson renormalization group equations can be formulated as a functional Fokker-Planck equation in the infinite-dimensional configuration space of a field theory, suggesting a stochastic process in the space of couplings.…