Abstract
Given an amalgam of groups
then every quantum logicQ 0 = (L 0,M 0) (L 0 is aσ-orthomodular poset,M 0 is a full set of states on it) satisfying some reasonable conditions can be embedded in a quantum logicQ = (L, M), in which (1) all the automorphisms ofL form a group ∼-G 1, (2) all the automorphisms ofM form a group ∼-G 2, and (3) all the symmetries ofQ form a group ∼-G 0. The quantum logic of all closed subspaces of a Hilbert spaceH and all its measures satisfies the conditions required fromQ 0; hence, enlarging it, one can obtain “anything.”
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Trnková, V. Automorphisms and symmetries of quantum logics. Int J Theor Phys 28, 1195–1214 (1989). https://doi.org/10.1007/BF00669342
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DOI: https://doi.org/10.1007/BF00669342