Asymptotic completeness in nonrelativistic quantum field theory
type: Item
instance of: scholarly article
title: Asymptotic completeness in nonrelativistic quantum field theory
zbMATH Open document ID: 0905.47008
DOI: 10.1016/S0034-4877(97)85895-8
published in: Reports on Mathematical Physics
publication date: 1999-01-10T00:00:00Z
review text: The contents of the invited lecture to the XXIX Symposium on Mathematical Physics, Toruń, 3-6 December, 1996. Two simple nonrelativistic quantum field theory models of mathematical scattering theory are considered. The goal is to show asymptotic completeness for both models. The first model is called by the author ``standard model of nonrelativistic matter''. It describes a system of particles which are divided into species and are identical within each species, subject to either bosonic or fermionic statistics. The model preserves the number of particles of each species and is Galilean-covariant. The theorem of asymptotic completeness of the system is stated whose proof can be reduced to the corresponding theorem for \(N\)-body Schrödinger operators. The detail consideration is expected to appear in Rev. Math. Phys. The second model sometimes called Pauli-Fierz Hamiltonian describes a small spatially confined system such as an atom or impurity interacting with free bosons (radiation, phonons, etc.). The model avoids the infra-red problem and is not translation-invariant but does not preserve the number of particles. The proof of asymptotic completeness for the model is being prepared for publication.
Mathematics Subject Classification ID: 47A40
Mathematics Subject Classification ID: 81T10
Mathematics Subject Classification ID: 81U10
Mathematics Subject Classification ID: 47N50
Mathematics Subject Classification ID: 81Q10
zbMATH DE Number: 1158132
zbMATH Keywords: asymptotic completeness
zbMATH Keywords: nonrelativistic quantum field theory models
zbMATH Keywords: \(N\)-body scattering
zbMATH Keywords: mathematical scattering theory
zbMATH Keywords: standard model of nonrelativistic matter
zbMATH Keywords: Galilean-covariant
zbMATH Keywords: \(N\)-body Schrödinger operators
zbMATH Keywords: Pauli-Fierz Hamiltonian model
zbMATH Keywords: free bosons
zbMATH Keywords: radition
zbMATH Keywords: phonons
author: Jan Dereziński
reviewed by: Pavel Dyshlovenko
MaRDI profile type: Publication
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full work available at URL: s0034-4877(97)85895-8
OpenAlex ID: W2007069894
description: scientific article; zbMATH DE number 1158132