Scaling limits of integrable quantum field theories
type: Item
instance of: scholarly article
zbMATH Open document ID: 1246.81093
DOI: 10.1142/S0129055X11004539
author: Henning Bostelmann
author: Gandalf Lechner
author: Gerardo Morsella
published in: Reviews in Mathematical Physics
publication date: 2012-06-13T00:00:00Z
full work available at URL: https://arxiv.org/abs/1105.2781
Mathematics Subject Classification ID: 81T05
Mathematics Subject Classification ID: 81T17
Mathematics Subject Classification ID: 47C15
Mathematics Subject Classification ID: 81T40
Mathematics Subject Classification ID: 81R15
Mathematics Subject Classification ID: 46L60
zbMATH DE Number: 6045733
zbMATH Keywords: ultraviolett scaling
zbMATH Keywords: two-dimensional quantum fields
zbMATH Keywords: algebraic quantum field theory
zbMATH Keywords: wedge-local quantum fields
zbMATH Keywords: massless scaling limits
MaRDI profile type: Publication
arXiv ID: 1105.2781
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OpenAlex ID: W3100107963
title: Scaling limits of integrable quantum field theories
review text: Modern theory of non-perturbative renormalization is at the core of many achievements of contemporary physics. Historically, the renormalization group technique had its origin in scale invariance. The requirement that scattering amplitudes are independent of our choice of the energy scale at which the theory is renormalized lead to the Callan-Symanzik equation from 1970. The most important application of computing the large energy limit is the asymptotic freedom of quantum chromodynamics. In the present article the authors study the scaling limit of a class of integrable models in 1+1-dimensional space-time. It is interesting to note that two-dimensional sigma models share with QCD the property of asymptotic freedom. There exist many different approaches to obtaining scaling limits. Within the context of algebraic quantum field theory, Buchholz and Verch reconsidered the renormalization group and introduced so-called scaling algebras. One can also make use of so-called wedge-local quantum field, i.e. fields that are localized in infinite wedge-shaped space-time regions. The algebraic as well as the wedge technique is used in the present article. It is shown that limit theories exist for integrable field theories. They disintegrate into tensor products of chiral field theories covariant under translations. Consider now observables that are localized in finite light ray intervals. On the subspace generated by applying these observables to the vacuum, this dilation symmetry can be extended to the Möbius group, i.e. the scaling limit extends to a conformal quantum field on the circle.
reviewed by: Gert Roepstorff
description: scientific article; zbMATH DE number 6045733