On the mathematical foundations of quantum theory

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dc.contributor.authorCharlwood, Gerald Williamen_US
dc.date.accessioned2024-08-13T17:47:24Z
dc.date.available2024-08-13T17:47:24Z
dc.date.copyright1981en_US
dc.date.issued1981
dc.degree.departmentDepartment of Mathematics
dc.degree.departmentDepartment of Mathematics and Statistics
dc.degree.levelMaster of Science M.Sc.en
dc.description.abstractBeginning 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.en_US
dc.format.extent63 pages
dc.identifier.urihttps://hdl.handle.net/1828/17462
dc.rightsAvailable to the World Wide Weben_US
dc.titleOn the mathematical foundations of quantum theoryen_US
dc.typeThesisen_US

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