On the mathematical foundations of quantum theory
Date
1981
Authors
Charlwood, Gerald William
Journal Title
Journal ISSN
Volume Title
Publisher
Abstract
Beginning with the work of Birkhoff and von Neumann, the lattice of closed subspaces of Hilbert space has been studied by mathematicians, physicists, and philosophers. Since the 1960's, work of Gudder and of Kochen has focussed on partial structures extracted from, or related to, the lattice mentioned above.
This thesis follows in the same tradition. Starting from a new point of view, a particular sort of partial algebra is constructed. The relations of these structures, quasi boolean algebras, to Gudder's work on various sorts of posets and lattices are studied. Their relation to the partial boolean algebras studied by Kochen is also described. In this connection, his definition of partial boolean algebras is refined.
A study of quasi boolean algebras themselves is started. Various properties of these partial algebras are isolated and studied. The theory of relations between these partial algebras is then investigated. This theory is modelled after both standard developments in quantum mechanics proper, and some recent work by Kochen. In particular, a theory of "projections" and "interactions" in the context of these algebras is begun.