Semimodularity and the logic of quantum mechanics |
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Authors: | James C. T. Pool |
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Affiliation: | (1) Institut de Physique Théorique, Université de Genève Applied Mathematics Division, Argonne National Laboratory, Switzerland;(2) Department of Mathematics, University of Massachusetts, 01002 Amherst, Massachusetts, USA |
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Abstract: | If (, ,P, ) is an event-state-operation structure, then the events form an orthomodular ortholattice (, , ) and the operations, mappings from the set of states into , form a Baer *-semigroup (S, , *, ). Additional axioms are adopted which yield the existence of a homomorphism from (S, , *, ) into the Baer *-semigroup (S(), , *, ) of residuated mappings of (, , ) such thatx S maps states while x S () maps supports of states. If (, , ) is atomic and there exists a correspondence between atoms and pure states, then the existence of provides the result: (, , ) is semimodular if and only if every operationx S is a pure operation (maps pure states into pure states).Supported in part by the United States Atomic Energy Commission and in part by the Fonds National Suisse. |
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