Renormalization group analysis of spectral problems in quantum field theory
type: Item
instance of: scholarly article
title: Renormalization group analysis of spectral problems in quantum field theory
zbMATH Open document ID: 0923.47041
author: Volker Bach
author: Jürg Fröhlich
author: I. M. Sigal
published in: Advances in Mathematics
publication date: 1998-10-26T00:00:00Z
review text: A new renormalization group technique is described in detail and mathematically selfcontained. In this theory, the renormalization group transformation acts directly on a space of operators. Spectral properties of Hamiltonians are studied which generate the time evolution of atomic systems with electrons bound to static nuclei and interacting with a quantized radiation field. It is shown e.g. when excited atomic states turn into resonances. The topics in the sections of this article are: Description of the model and spectral results, the analysis of Feshbach maps, elimination of particle- and high photon-energy degrees of freedom, description of an inductive renormalization group construction and their spectral consequences.
reviewed by: Michael Demuth
Mathematics Subject Classification ID: 47N50
Mathematics Subject Classification ID: 81T15
zbMATH DE Number: 1215512
zbMATH Keywords: spectral properties of Hamiltonians
zbMATH Keywords: renormalization group technique
zbMATH Keywords: excited atomic
zbMATH Keywords: resonances
zbMATH Keywords: Feshbach maps
MaRDI profile type: Publication
full work available at URL: aima.1998.1733
OpenAlex ID: W2037555479
cites work: Mathematical theory of nonrelativistic matter and radiation
cites work: Quantum electrodynamics of confined nonrelativistic particles
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cites work: Q3671491
cites work: Introduction to spectral theory. With applications to Schrödinger operators
cites work: Q4110164
cites work: Q3286217
cites work: Q4185363
DOI: 10.1006/AIMA.1998.1733
description: scientific article; zbMATH DE number 1215512