Related papers: A Short Lecture on Divergences
The review presents general methods for treating complicated problems that cannot be solved exactly and whose solution encounters two major difficulties. First, there are no small parameters allowing for the safe use of perturbation theory…
We review the method of differential renormalization, paying special attention to a new constrained version for symmetric theories.
This paper is based on a course given by the author at the University of Rome ``La Sapienza'' in the Academic year 2000/2001. The intended aim of the course was to rapidly introduce, although not in an exhaustive way, the non-expert PhD…
We investigate to what extent renormalization can be understood as an algebraic manipulation on concatenated one-loop integrals. We find that the resulting algebra indicates a useful connection to knot theory as well as number theory and…
A bibliographic database containing studies on recurrence plots and related methods is analyzed from various perspectives. This allows a detailed view of the field's development, showcasing the continuous growth in the method's popularity,…
In theories with branes, bulk fields get in general divergent corrections localized on these defects. Hence, the corresponding brane terms are renormalized and should be included in the effective theory from the very beginning. We review…
The relation between renormalization and short distance singular divergencies in quantum field theory is studied. As a consequence a finite theory is presented. It is shown that these divergencies are originated by the multiplication of…
We apply the renormalization group theory to the dynamical systems with the simplest example of basic biological motifs. This includes the interpretation of complex networks as the perturbation to simple network. This is the first step to…
Basic elements of the exact renormalization group method and recent results within this approach are reviewed. Topics covered are the derivation of equations for the effective action and relations between them, derivative expansion,…
Based on our studies done on two-dimensional autonomous systems, forced non-autonomous systems and time-delayed systems, we propose a unified methodology - that uses renormalization group theory - for finding out existence of periodic…
A personal and subjective recollection, concerning mainly Wilson's lectures delivered over the spring of 1972 at Princeton University (summary of a talk at Cornell University on November 16, 2013 at the occasion of the memorial Kenneth G.…
These lecture notes evolve around mathematical concepts arising in inverse problems. We start by introducing inverse problems through examples such as differentiation, deconvolution, computed tomography and phase retrieval. This then leads…
These lecture notes concern information-theoretic notions of entropy. They are intended for, and have been successfully taught to, undergraduate students interested inresearch careers. Besides basic notions of analysis related to…
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…
An elementary introduction to the non-perturbative renormalization group is presented mainly in the context of statistical mechanics. No prior knowledge of field theory is necessary. The aim is this article is not to give an extensive…
Correlators describing the vulcanization transition are constructed and explored via a renormalization group approach. This approach is based on a minimal model that accounts for the thermal motion of constituents and the quenched random…
I review the theory of renormalization, as applied to weak-coupling perturbation theory in quantum field theories.
Percolation refers to an interesting class of problems related to the properties of disordered systems, usually formulated in terms of objects randomly placed on an underlying lattice or continuum. Despite the simplicity of the setup, most…
Recently delivered lectures on Self-Referential Mathematics, [2], at the Department of Mathematics and Applied Mathematics, University of Pretoria, are briefly presented. Comments follow on the subject, as well as on Inconsistent…
We review recent developments in the theory of renormalisation group flows in minimal models with boundaries. Among these, we discuss in particular the perturbative calculations of Recknagel et al, not only as a tool to predict the IR…