A theory of scattering for quasifree particles
type: Item
instance of: scholarly article
zbMATH Open document ID: 1304.81003
DOI: 10.1142/9192
author: Raymond F. Streater
publication date: 2014-10-27T00:00:00Z
Mathematics Subject Classification ID: 81-02
Mathematics Subject Classification ID: 81U05
Mathematics Subject Classification ID: 81T10
Mathematics Subject Classification ID: 81V10
Mathematics Subject Classification ID: 46L60
zbMATH DE Number: 6361943
zbMATH Keywords: scattering theory
zbMATH Keywords: quasifree quantum fields
zbMATH Keywords: quantum electrodynamics
zbMATH Keywords: Haag-Kastler Axioms
zbMATH Keywords: photon field
zbMATH Keywords: Weyl Relations
zbMATH Keywords: vanishing connected time-ordered products
zbMATH Keywords: euclidean electrodynamics
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1142/9192
OpenAlex ID: W578681607
title: A theory of scattering for quasifree particles
review text: Many theoretical physicists agree that is very difficult to construct and renormalize interacting quantum field theories using the framework of Wightman axioms. Some believe that it may be appropriate to start with an approximation, perhaps with some cut-off at large energy, so that modes with larger energy do not interact. Some physicists have generalized the Wightman framework. In particular, Streater points at questions related to a possible nonexistence of quantum electrodynamics in a strict sense. In his book he suggests a way around these problems, using unusual representations of the \(C^*\)-algebra of observables as inspired by Donaldson. Streater allows non-square integrability and so giving rise to a flat connection on the sheaf of electromagnetic fields, similar to the use of cocycles found by Doplicher and Roberts in the context of Haag-Kastler axioms. The main idea then is to introduce quasifree representations of the photon field. A quasifree quantum field is one with zero as the value of any connected time-ordered product of quantum fields. The book has eight chapters. Chapter 1 gives an introduction, Chapter 2 provides the Haag-Kastler Axioms, and Chapter 3 the representations of the Poincaré Group. Chapter 4 discusses the Maxwell Field, Chapter 5 certain representations, i.e. Weyl Relations, coherent states and the Segal-Bargmann Transform. Chapter 6 explains Euclidean Electrodynamics and the Nelson Axioms while Chapter 7 discusses certain models such as instantons, magnetic poles an solitons. A summary and conclusions may be found in Chapter 8.
reviewed by: Gert Roepstorff
description: scientific article; zbMATH DE number 6361943