States on orthoalgebras
type: Item
instance of: scholarly article
title: States on orthoalgebras
zbMATH Open document ID: 0841.03034
DOI: 10.1007/BF00676255
author: Mirko Navara
author: Jan Hamhalter
author: Pavel Pták
published in: International Journal of Theoretical Physics
publication date: 1996-07-16T00:00:00Z
review text: An orthoalgebra is a quadruple \((L, 0, 1, \oplus)\) where \(L\) is a set, \(0,1\in L\) and \(\oplus\) is a partial binary operation on \(L\) such that (i) whenever one side of the commutativity or associativity law (for \(\oplus\)) is defined then so is the other and both sides are equal, (ii) for every \(a\in L\) there exists a unique \(b\in L\) with \(a\oplus b=1\), and (iii) 0 is the unique element \(a\) of \(L\) for which \(a\oplus a\) exists. Orthoalgebras can be considered as generalizations of orthomodular posets by interpreting \(\oplus\) as the join of orthogonal elements. It turned out that orthoalgebras are appropriate structures within the logico-algebraic foundation of quantum theories. States (i.e. finitely additive normed measures) on orthoalgebras are considered and a pasting technique for orthoalgebras is developed by means of which orthoalgebras are constructed whose state space has certain preassigned properties. The problem of extending states to larger orthoalgebras is also investigated.
reviewed by: Helmut Länger
Mathematics Subject Classification ID: 03G12
zbMATH DE Number: 844070
zbMATH Keywords: orthoalgebra
zbMATH Keywords: join of orthogonal elements
zbMATH Keywords: pasting
zbMATH Keywords: state space
zbMATH Keywords: extending states
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf00676255
OpenAlex ID: W2033189951
description: scientific article; zbMATH DE number 844070