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Baser*-semigroups and the logic of quantum mechanics

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Abstract

The theory of orthomodular ortholattices provides mathematical constructs utilized in the quantum logic approach to the mathematical foundations of quantum physics. There exists a remarkable connection between the mathematical theories of orthomodular ortholattices and Baer*-semigroups; therefore, the question arises whether there exists a phenomenologically interpretable role for Baer *-semigroups in the context of the quantum logic approach. Arguments, involving the quantum theory of measurements, yield the result that the theory of Baer *-semigroups provides the mathematical constructs for the discussion of “operations” and conditional probabilities.

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Authors and Affiliations

  1. II. Institut für Theoretische Physik, Universität Hamburg, Germany

    James C. T. Pool

  2. Applied Mathematics Division, Argonne National Laboratory, 60439, Argonne, Ill.

    James C. T. Pool

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  1. James C. T. Pool
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Supported in part by the United States Atomic Energy Commission.

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Pool, J.C.T. Baser*-semigroups and the logic of quantum mechanics. Commun.Math. Phys. 9, 118–141 (1968). https://doi.org/10.1007/BF01645838

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  • DOI: https://doi.org/10.1007/BF01645838

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