Field algebras do not leave field domains invariant
type: Item
instance of: scholarly article
title: Field algebras do not leave field domains invariant
zbMATH Open document ID: 0597.47028
DOI: 10.1007/BF01221653
author: S. S. Khoruzhij
author: A. V. Voronin
published in: Communications in Mathematical Physics
publication date: 1986-01-01T00:00:00Z
review text: It is proved that von Neumann algebras associated to \(Op^*\)-algebra (P,D) cannot leave the domain D of P invariant if they are type I or type III factors or finite direct sums of such factors. The class of \(Op^*\)- algebras for which this result holds includes, in particular, all (P,D) generated by essentially self-adjoint operators or such that \(P_ s'=P_ w'\) (resp. the strong and the weak bounded commutants of P); the only condition on the von Neumann algebra R is \(R\supset (P_ w')'\). The result is applied to quantum field systems described by Wightman fields A(f) with the definition domain D and von Neumann field algebras, global F and local F(0). It gives that in typical cases (in particular, for all free fields) the field algebras F and F(0) do not leave D invariant, and also that the Op\({}^*\)-algebras generated by Wightman fields cannot belong to some simplest classes of \(Op^*\)-algebras, like \(SV^*\) or closed \(EW^*\)-algebras.
Mathematics Subject Classification ID: 47L60
Mathematics Subject Classification ID: 47L90
Mathematics Subject Classification ID: 46L05
Mathematics Subject Classification ID: 81T05
zbMATH DE Number: 3962549
zbMATH Keywords: von Neumann algebras
zbMATH Keywords: essentially self-adjoint operators
zbMATH Keywords: bounded commutants
zbMATH Keywords: quantum field systems
zbMATH Keywords: von Neumann field algebras
zbMATH Keywords: \(Op^*\)- algebras generated by Wightman fields
MaRDI profile type: Publication
cites work: Algebras of unbounded operators and vacuum superselection rules in quantum field theory. I. Some properties of \(Op^*\) algebras and vector states on them
cites work: V*-algebras: A particular class of unbounded operator algebras
full work available at URL: https://doi.org/10.1007/bf01221653
OpenAlex ID: W2077907338
description: scientific article; zbMATH DE number 3962549