Foundations of Physics

, Volume 1, Issue 2, pp 173–182 | Cite as

On the logical structure of quantum mechanics

  • G. T. Rüttimann
Article

Abstract

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.

Keywords

Quantum Mechanic Special Structure Logical Structure Central Importance Mathematical Foundation 

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References

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    J. C. T. Pool, Baer *-semigroup and the logic of quantum mechanics,Commun. Math. Phys. 9, 118 (1968).Google Scholar

Copyright information

© Plenum Publishing Corporation 1970

Authors and Affiliations

  • G. T. Rüttimann
    • 1
  1. 1.Institute of Theoretical PhysicsUniversity of BerneBerneSwitzerland

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