Croc lattices are of central importance in the mathematical foundation of quantum mechanics. They reflect the structure of the logical calculus of propositions concerning microphenomena. In this context, the mathematical consequences resulting from the special structure of the lattice are of particular interest. Beginning with the notion of hemimorphism of a croc lattice, we get, in a natural way, an extension of the structure of the lattice by the Baer *-semigroup. We embed the Baer *-semigroup in an algebra with generalized *- and ′-operations and prove some theorems as consequences of the particular properties of the underlying croc lattice.
KeywordsQuantum Mechanic Special Structure Logical Structure Central Importance Mathematical Foundation
Unable to display preview. Download preview PDF.
- 1.P. Mittelstaedt, Quantenlogik,Fortschr. Physik 9, 106 (1961).Google Scholar
- 2.C. Piron, Axiomatique quantique,Helv. Phys. Acta 37, 439 (1964).Google Scholar
- 3.D. J. Foulis, Baer *-semigroups,Proc. Am. Math. Soc. 11, 648 (1960).Google Scholar
- 4.J. C. T. Pool, Baer *-semigroup and the logic of quantum mechanics,Commun. Math. Phys. 9, 118 (1968).Google Scholar