Scale-dependent functions, stochastic quantization and renormalization
type: Item
instance of: scholarly article
title: Scale-dependent functions, stochastic quantization and renormalization
zbMATH Open document ID: 1095.81040
DOI: 10.3842/SIGMA.2006.046
published in: SIGMA. Symmetry, Integrability and Geometry: Methods and Applications
publication date: 2006-07-04T00:00:00Z
full work available at URL: https://arxiv.org/abs/hep-th/0604170
full work available at URL: https://eudml.org/doc/52658
full work available at URL: index.html
review text: This paper studies the possibility to unify some methods of regularization, such as the renormalization group method, stochastic quantization etc., by means of an extension of the standard field theory of the square-integrable functions \(\phi(b) \in L^2(R^d)\) to the theory of functions depending on the coordinate \(b\) and ``resolution'' parameter \(a\). In the simplest case such field theory turns out to be a theory of fields \(\phi_a(b,\cdot)\) defined on the affine group \(G\) of the maps \(x\mapsto x' = ax+b\), \(a > 0\), \(x, b \in R^d\), which consists of dilations and translation of Euclidean space. The fields \(\phi_a(b,\cdot)\) are obtained making use of the continuous wavelet transform. The parameters of the theory may explicitly depend on the resolution \(a\). A suitable choice of the scale dependence \(g = g(a)\) makes such theory free of divergences by construction.
Mathematics Subject Classification ID: 81S20
Mathematics Subject Classification ID: 81T16
Mathematics Subject Classification ID: 42C40
Mathematics Subject Classification ID: 81S30
Mathematics Subject Classification ID: 81T17
zbMATH DE Number: 5038688
zbMATH Keywords: wavelets
zbMATH Keywords: quantum field theory
zbMATH Keywords: stochastic quantization
zbMATH Keywords: renormalization
author: Mikhail V. Altaisky
reviewed by: Valter Moretti
MaRDI profile type: Publication
arXiv ID: hep-th/0604170
Recommended article: Q3703040
Recommended article: Probabilistic renormalization and analytic continuation
Recommended article: Q4853608
Recommended article: Q4853606
Recommended article: Q4853607
Recommended article: Renormalization group and probability theory
Recommended article: Q3718312
Recommended article: Renormalization group and stochastic PDEs
Recommended article: Q4853617
Recommended article: Stochastic quantization of field theory in finite and infinite volume
description: scientific article