Independence of automorphism group,center, and state space of quantum logics |
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Authors: | Mirko Navara |
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Affiliation: | (1) Department of Mathematics, Faculty of Electrical Engineering, Technical University of Prague, 166 27 Prague 6, Czechoslovakia |
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Abstract: | We prove that quantum logics (=orthomodular posets) admit full independence of the attributes important within the foundations of quantum mechanics. Namely, we present the construction of quantum logics with given sublogics (=physical subsystems), automorphism groups, centers (=classical parts of the systems), and state spaces. Thus, all these parameters are independent. Our result is rooted in the line of investigation carried out by Greechie; Kallus and Trnková; Kalmbach; and Navara and Pták; and considerably enriches the known algebraic methods in orthomodular posets. |
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