Related papers: Renormalization: general theory
Renormalization procedure is generalized to be applicable for non renormalizable theories. It is shown that introduction of an extra expansion parameter allows to get rid of divergences and express physical quantities as series of finite…
Satisfiability is a classic problem in computational complexity theory, in which one wishes to determine whether an assignment of values to a collection of Boolean variables exists in which all of a collection of clauses composed of logical…
It is shown that the renormalization group method does not necessarily eliminate all secular terms in perturbation series to partial differential equations and a functional subspace of renormalizable secular solutions corresponds to a…
Renormalization group method is one of the most powerful tool to obtain approximate solutions to differential equations. We apply the renormalization group method to Hamiltonian systems whose integrable parts linearly depend on action…
We give a systematic, abstract formulation of the image normalization method as applied to a general group of image transformations, and then illustrate the abstract analysis by applying it to the hierarchy of viewing transformations of a…
A careful analysis of differential renormalization shows that a distinguished choice of renormalization constants allows for a mathematically more fundamental interpretation of the scheme. With this set of a priori fixed integration…
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…
In these notes the exact renormalization group formulation of the scalar theory is briefly reviewed. This regularization scheme is then applied to supersymmetric theories. In case of a supersymmetric gauge theory it is also shown how to…
After a brief presentation of the exact renormalization group equation, we illustrate how the field theoretical (perturbative) approach to critical phenomena takes place in the more general Wilson (nonperturbative) approach. Notions such as…
We present several approaches to renormalization in QFT: the multi-scale analysis in perturbative renormalization, the functional methods \`a la Wetterich equation, and the loop-vertex expansion in non-perturbative renormalization. While…
We review current progress in the functional renormalization group treatment of disordered systems. After an elementary introduction into the phenomenology, we show why in the context of disordered systems a functional renormalization group…
In this article, I give a pedagogical introduction and overview of percolation theory. Special emphasis will be put on the review of some of the most prominent of the algorithms that have been devised to study percolation numerically. At…
We give a review of three works on the construction of random models for singular stochastic partial differential equations within the theory of regularity structures.
A recently introduced real space renormalization group technique, developed for the analysis of processes in the Kardar-Parisi-Zhang universality class, is generalized and tested by applying it to a different family of surface growth…
We present an overview of the Density Matrix Renormalization Group and its connections to Quantum Groups, Matrix Products and Conformal Field Theory. We emphasize some common formal structures in all these theories. We also propose…
We start with a simple introduction into the renormalization group (RG) in quantum field theory and give an overview of the renormalization group method. The third section is devoted to essential topics of the renorm-group use in the QFT.…
Recent progress concerning regularization of supersymmetric theories is reviewed. Dimensional reduction is reformulated in a mathematically consistent way, and an elegant and general method is presented that allows to study the…
A short review of recent renormalization group analyses of the self-consistence of the Standard Model is presented.
Resummation, ie. reorganization of perturbative series, can result in an inconsistent perturbation theory, unless the counterterms are reorganized in an appropriate way. In this paper two methods are presented for resummation of…
A perturbative description of Large Scale Structure is a cornerstone of our understanding of the observed distribution of matter in the universe. Renormalization is an essential and defining step to make this description physical and…