Related papers: Exponential renormalization
We present a method of calculating the interacting S-matrix to an arbitrary perturbative order for a large class of boson interaction Lagrangians. The method takes advantage of a previously unexplored link between the $n$-point Green's…
We describe various combinatorial aspects of the Birkhoff-Connes-Kreimer factorization in perturbative renormalisation. The analog of Bogoliubov's preparation map on the Lie algebra of Feynman graphs is identified with the pre-Lie Magnus…
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…
In the Hopf algebra approach of Connes and Kreimer on renormalization of quantum field theory, the renormalization process is views as a special case of the Algebraic Birkhoff Decomposition. We give a differential algebra variation of this…
We describe a unification of several apparently unrelated factorizations arisen from quantum field theory, vertex operator algebras, combinatorics and numerical methods in differential equations. The unification is given by a Birkhoff type…
Functional Renormalization Group Equations constitute a powerful tool to encode the perturbative and non-perturbative properties of a physical system. We present an algorithm to systematically compute the expansion of such flow equations in…
We extend the Hopf algebra description of a simple quantum system given previously, to a more elaborate Hopf algebra, which is rich enough to encompass that related to a description of perturbative quantum field theory (pQFT). This provides…
We give a proof of the convergence of the BHZ renormalized model associated with the generalized (KPZ) equation that does not require the full strength of the BPHZ renormalisation. Our approach is based on a convenient form of chaos…
In a previous paper "Anomalies in Quantum Field Theory and Cohomologies of Configuration Spaces" (arXiv:0903.0187) we presented a new method for renormalization in Euclidean configuration spaces based on certain renormalization maps. This…
Renormalization is a powerful technique in statistical physics to extract the large-scale behavior of interacting many-body models. These notes aim to give an introduction to perturbative methods that operate on the level of the stochastic…
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…
We provide a self-contained formulation of the BPHZ theorem in the Euclidean context, which yields a systematic procedure to "renormalise" otherwise divergent integrals appearing in generalised convolutions of functions with a singularity…
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…
We propose several exponential inequalities for self-normalized martingales similar to those established by De la Pe\~{n}a. The keystone is the introduction of a new notion of random variable heavy on left or right. Applications associated…
Different perturbation theory treatments of the Ginzburg-Landau phase transition model are discussed. This includes a criticism of the perturbative renormalization group (RG) approach and a proposal of a novel method providing critical…
In this work a general approach to compute a compressed representation of the exponential $\exp(h)$ of a high-dimensional function $h$ is presented. Such exponential functions play an important role in several problems in Uncertainty…
A perturbative approach for non renormalizable theories is developed. It is shown that the introduction of an extra expansion parameter allows one to get rid of divergences and express physical quantities as series with finite coefficients.…
Following Manin's approach to renormalization in the theory of computation, we investigate Dyson-Schwinger equations on Hopf algebras, operads and properads of flow charts, as a way of encoding self-similarity structures in the theory of…
We apply Feshbach-Krein-Schur renormalization techniques in the hierarchical Anderson model to establish a criterion on the single-site distribution which ensures exponential dynamical localization as well as positive inverse participation…
The Rota-Baxter operator and the modified Rota-Baxter operator on various algebras are both important in mathematics and mathematical physics. The former is originated from the integration-by-parts formula and probability with applications…