Axiomatic quantum theory

Journal of Philosophical Logic 30 (5):465-477 (2001)
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Abstract

The basis of a rigorous formal axiomatization of quantum mechanics is constructed, built upon Dirac's bra-ket notation. The system is three-sorted, with separate variables for scalars, vectors and operators. First-order quantification over all three types of variable is permitted. Economy in the axioms is effected by, e.g., assigning a single logical function * to transform (i) a scalar into its complex conjugate, (ii) a ket vector into a bra and a bra into a ket, (iii) an operator into its adjoint. The system is accompanied by a formal semantics. Further papers will deal with vector subspaces and projection operators, operators with continuous spectra, tensor products, observables, and quantum mechanical probabilities

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Storrs McCall
McGill University

Citations of this work

Scientific Theories, Models and the Semantic Approach.Otávio Bueno & Décio Krause - 2007 - Principia: An International Journal of Epistemology 11 (2):187-201.
Scientific Theories, Models and the Semantic Approach.Krause Décio & Bueno Otávio - 2007 - Principia: An International Journal of Epistemology 11 (2):187-201.

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References found in this work

Principia mathematica.A. N. Whitehead - 1926 - Mind 35 (137):130.
Begriffsschrift.Gottlob Frege - 1967 - In Jean Van Heijenoort (ed.), From Frege to Gödel. Cambridge: Harvard University Press. pp. 1-83.
From Frege to Gödel.Jean van Heijenoort - 1968 - Philosophy of Science 35 (1):72-72.
Axiomatic Set Theory.Alfons Borgers - 1960 - Journal of Symbolic Logic 25 (3):277-278.

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