Baer *-semigroups and the logic of quantum mechanics

James T. Pool

pp. 365-394

in: Clifford A. Hooker (ed), The logico-algebraic approach to quantum mechanics I, Berlin, Springer, 1975

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.