Related papers: An etude on a renormalization
There is growing body of learning problems for which it is natural to organize the parameters into matrix, so as to appropriately regularize the parameters under some matrix norm (in order to impose some more sophisticated prior knowledge).…
We develop a formalism for performing real space renormalization group transformations of the "decimation type" using perturbation theory. The type of transformations beyond $d=1$ is nontrivial even for free theories. We check the formalism…
We consider the application of regularization by dimensional reduction to NLO corrections of hadronic processes. The general collinear singularity structure is discussed, the origin of the regularization-scheme dependence is identified and…
A class of exact infinitesimal renormalization group transformations is proposed and studied. These transformations are pure changes of variables (i.e., no integration or elimination of some degrees of freedom is required) such that a…
Using an infinitesimal approach, this work addresses the renormalization problem to deal with the ultraviolet divergences arising in quantum field theory. Under the assumption that the action has already been renormalized to yield an…
In the present work we shall describe and apply the techniques of the Renormalization Group - based in data rescaling and operator renormalizing - and of Homogenization - that substitutes, in a certain limit, a periodically inhomogeneous…
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…
In recent work we have developed a renormalization framework for stabilizing reduced order models for time-dependent partial differential equations. We have applied this framework to the open problem of finite-time singularity formation…
Recent work on the use of dimensional reduction for the regularisation of non--supersymmetric theories is reviewed. It is then shown that there exists a class of theories for which a universal form of the soft supersymmetry breaking terms…
We propose a theoretical formulation of protected edge modes in the language of quantum field theories based on the contemporary understanding of the renormalization group. We use bulk and boundary renormalization arguments which have never…
The paper is devoted to the methods of solving simultaneous recurrences. Specifically, we discuss transformation of matrix recurrences to regular recurrences and propose a way of solving special matrix recurrences of order three by their…
We study the renormalization of normal mixing matrices, which includes hermitian and unitary matrices as particular cases. We give a minimal, multiplicative parametrization of counterterms, and compute the renormalized Lagrangian to…
We develop a scaling theory and a renormalization technique in the context of the modern theory of polarization. The central idea is to use the characteristic function (also known as the polarization amplitude) in place of the free energy…
We introduce a new regularization scheme for divergent integrals in quantum field theory. The framework is based on the structural decomposition of the integrand asymptotic expansion, which distinguishes between contributions that drive UV…
We incorporate running parameters and anomalous dimensions into the framework of the exact renormalization group. We modify the exact renormalization group differential equations for a real scalar field theory, using the anomalous…
Methods for the reduction of the complexity of computational problems are presented, as well as their connections to renormalization, scaling, and irreversible statistical mechanics. Several statistically stationary cases are analyzed; for…
The renormalization group method is a successive integration over the fluctuations which are ordered according to their length scale, a parameter in the external space. A different procedure is described, where the fluctuations are treated…
We study a renormalizable four dimensional model with two deformed quantized space directions. A one-loop renormalization is performed explicitly. The Euclidean model is connected to the Minkowski version via an analytic continuation. At a…
The possible usefulness of the renormalization group method in Nuclear Physics is pointed out in this talk in the context of the nuclear multifragmentation. The presentation is rather superficial and sketchy, to indicate the main lines…
We study the dynamics of the renormalization operator for multimodal maps. In particular, we prove the exponential convergence of this operator for infinitely renormalizable maps with same bounded combinatorial type.