An approach to the foundations of quantum mechanics, using the concept of a filter as a primitive / Hans Kummer

Auteur: Kummer, Hans (1936-) - AuteurType de document: MonographieCollection: Queen's papers in pure and applied mathematics ; 70Langue: anglaisPays: CanadaÉditeur: Kingston, Ontario : Queen's University, 1984Description: 1 vol. (pagin. multiple) ; 28 cmNote: It is shown that the Jordan structure of non-relativistic quantum theory can be deduced, at least in the finite-dimensional case, from four physically clear postulates. The axiomatic approach to the foundations of quantum mechanics developed here takes the concept of a filter as a starting point. More precisely, the primitive notions of the theory are: probability, filter, composition of filters, and stochastic selection of filters. All filters are assumed to be built from a countable set of primitive filters by composition and stochastic selection. Next, two physically transparent axioms are introduced, which allow the author to define the concept of a system (Definition 3.2). With every system there is associated a quadruple, the so-called σ-quadruple (Definition 3.10), whose first member is a separable complete order unit space. Then, two additional axioms are formulated, which lead to the effect that this space becomes isomorphic to the order unit space underlying a Jordan- Banach algebra, at least in the finite-dimensional case (Corollary 4.23). (Zentralblatt)Bibliographie: Bibliogr. p. [128-129]. Sujets MSC: 46Nxx Functional analysis -- Miscellaneous applications of functional analysis
17C65 Nonassociative rings and algebras -- Jordan algebras (algebras, triples and pairs) -- Jordan structures on Banach spaces and algebras
46H70 Functional analysis -- Topological algebras, normed rings and algebras, Banach algebras -- Nonassociative topological algebras
46B42 Functional analysis -- Normed linear spaces and Banach spaces; Banach lattices -- Banach lattices
81P10 Quantum theory -- Axiomatics, foundations, philosophy -- Logical foundations of quantum mechanics; quantum logic
Location Call Number Status Date Due
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It is shown that the Jordan structure of non-relativistic quantum theory can be deduced, at least in the finite-dimensional case, from four physically clear postulates. The axiomatic approach to the foundations of quantum mechanics developed here takes the concept of a filter as a starting point. More precisely, the primitive notions of the theory are: probability, filter, composition of filters, and stochastic selection of filters. All filters are assumed to be built from a countable set of primitive filters by composition and stochastic selection. Next, two physically transparent axioms are introduced, which allow the author to define the concept of a system (Definition 3.2). With every system there is associated a quadruple, the so-called σ-quadruple (Definition 3.10), whose first member is a separable complete order unit space. Then, two additional axioms are formulated, which lead to the effect that this space becomes isomorphic to the order unit space underlying a Jordan- Banach algebra, at least in the finite-dimensional case (Corollary 4.23). (Zentralblatt)

Bibliogr. p. [128-129]

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