Automorphisms and symmetries of quantum logics
type: Item
instance of: scholarly article
title: Automorphisms and symmetries of quantum logics
zbMATH Open document ID: 0697.03034
DOI: 10.1007/BF00669342
published in: International Journal of Theoretical Physics
publication date: 1989-01-01T00:00:00Z
review text: Let L be a quantum logic and let A(L) (S(L),C(L), resp.) denote the group of all automorphisms of L (the group of all symmetries of L, the group of all automorphisms of L which preserve the convex combinations of states, resp.). Then we have natural embeddings i: S(L)\(\to A(L)\) and e: S(L)\(\to C(L)\). Thus, with these embeddings, the triple S(L), A(L) and C(L) forms an amalgam of groups. The author raises the following interesting and highly nontrivial question: Given an amalgam of groups, can we always find its ``quantum logic'' representation as described above? She proves that we can. She also ensures that the representation enjoys properties significant within quantum theories. The proof she provides uses an advanced graph-theory technique.
Mathematics Subject Classification ID: 03G12
Mathematics Subject Classification ID: 81P10
Mathematics Subject Classification ID: 20B27
zbMATH DE Number: 4142030
zbMATH Keywords: state space of a quantum logic
zbMATH Keywords: automorphisms
zbMATH Keywords: symmetries
zbMATH Keywords: amalgam of groups
author: Věra Trnková
reviewed by: Pavel Pták
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf00669342
OpenAlex ID: W2003276859
description: scientific article; zbMATH DE number 4142030