Algebras of unbounded operators and vacuum superselection rules in quantum field theory. II. Mathematical structure of vacuum superselection rules
type: Item
instance of: scholarly article
title: Algebras of unbounded operators and vacuum superselection rules in quantum field theory. II. Mathematical structure of vacuum superselection rules
zbMATH Open document ID: 0599.47074
DOI: 10.1007/BF01017886
author: A. V. Voronin
author: V. N. Sushko
author: S. S. Khoruzhij
published in: Theoretical and Mathematical Physics
publication date: 1984-01-01T00:00:00Z
review text: The algebraic structure of quantum-field systems with vacuum superselection rules is analyzed in the framework of Wightman axiomatics on the basis of the mathematical formalism developed in Part I [ibid. 59, 28-48 (1984; Zbl 0559.47033)]. Two main theorems are obtained. The first asserts that a system with a discrete vacuum superselection rule, like systems with ordinary charge superselection rules, can always be described by a global algebra R of class P (direct sum of \(I_{\infty}\) type factors), and this property of the global algebra is equivalent to discreteness of the decomposition of the generating Wightman functional with respect to pure states, and also the existence of a discrete decomposition of the Hilbert space space into an orthogonal sum of vacuum superselection sectors. In accordance with the second theorem, there is a discrete vacuum superselection rule in all quantum-field systems for which the induction \(R'\to R'_{P_ 0}\), where \(P_ 0\) is the projection operator onto the vacuum subspace \({\mathcal H}_ 0\), has a discrete decomposition into irreducible elements (in particular, in all systems with finite-dimensional \({\mathcal H}_ 0)\). Other forms of vacuum structure in quantum field theory are analyzed.
Mathematics Subject Classification ID: 47L60
Mathematics Subject Classification ID: 46N99
Mathematics Subject Classification ID: 81T05
Mathematics Subject Classification ID: 47L90
zbMATH DE Number: 3967218
zbMATH Keywords: algebraic structure of quantum-field systems with vacuum superselection rules
zbMATH Keywords: Wightman axiomatics
zbMATH Keywords: discreteness of the decomposition of the generating Wightman functional with respect to pure states
zbMATH Keywords: existence of a discrete decomposition of the Hilbert space space into an orthogonal sum of vacuum superselection sectors
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3967218