Related papers: Renormalization: general theory
The perturbative quantization of gauge theories is shortly reviewed with emphasis of the local operator BRST-formalism.
We introduce a renormalization procedure which allows us to study in a unified and concise way different properties of the irrational rotations on the unit circle $\beta \mapsto \set{\alpha+\beta}$, $\alpha \in \R\setminus \Q$. In…
In recent years, a variety of learned regularization frameworks for solving inverse problems in imaging have emerged. These offer flexible modeling together with mathematical insights. The proposed methods differ in their architectural…
We revisit the renormalization group (RG) theoretical perturbation theory on oscillator-type second-order ordinary differential equations. For a class of potentials, we show a simple functional relation among secular coefficients of the…
We consider a possibility to unify the methods of regularization, such as the renormalization group method, stochastic quantization etc., by the extension of the standard field theory of the square-integrable functions $\phi(b)\in…
This review provides a detailed introduction to chiral gauge theories, renormalization theory, and the application of dimensional regularization with the non-anticommuting BMHV scheme for $\gamma_5$. One goal is to show how chiral gauge…
Two-loop renormalization group equations in gauge theories with multiple U(1) groups are presented. Instead of normalizing the abelian gauge fields in canonical forms, we retain kinetic-mixing terms and treat the mixing coefficients as free…
Renormalization plays an important role in the theoretically and mathematically careful analysis of models in condensed-matter physics. I review selected results about correlated-fermion systems, ranging from mathematical theorems to…
The history of renormalization is reviewed with a critical eye, starting with Lorentz's theory of radiation damping, through perturbative QED with Dyson, Gell-Mann & Low, and others, to Wilson's formulation and Polchinski's functional…
We discuss renormalization group approaches to strongly interacting Fermi systems, in the context of Landau's theory of Fermi liquids and functional methods, and their application to neutron matter.
We argue that the choice of an appropriate, massive, renormalization scheme can greatly improve the apparent convergence of perturbation theory at finite temperature. This is illustrated by the calculation of the pressure of a scalar field…
We relate renormalization in perturbative quantum field theory to the theory of limiting mixed Hodge structures using parametric representations of Feynman graphs.
The result from developing and applying the notions of functional self-similarity and the Bogoliubov renormalization group to boundary-value problems in mathematical physics during the last decade are reviewed. The main achievement is the…
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.
We develop an algorithmic, system-specific renormalization group (RG) procedure that is adapted from model reductions techniques from engineering control theory. The resulting "generalized" RG is a consistent generalization of the Wilsonian…
This lecture provides an introduction to the renormalisation group as applied to scattering of two nonrelativistic particles. As well as forming a framework for constructing effective theories of few-nucleon systems, these ideas also…
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.…
A block spin renormalization group approach is proposed for the dynamical triangulation formulation of quantum gravity in arbitrary dimensions. Renormalization group flow diagrams are presented for the three-dimensional and four-dimensional…
We formulate the infrared regularization of Becher and Leutwyler in a form analogous to our recently proposed extended on-mass-shell renormalization. In our formulation, IR regularization can be applied straightforwardly to multi-loop…
The renormalization group has proven to be a very powerful tool in physics for treating systems with many length scales. Here we show how it can be adapted to provide a new class of algorithms for discrete optimization. The heart of our…