Article Title：Axiomatic quantum theory
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 function (i) a scalar into its complex conjugate, (ii) a ket vector into a bra a 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.
Keywords: quantum mechanics; formal axiomatization
DOI: 10.1023/A:1012226116310
Source：JOURNAL OF PHILOSOPHICAL LOGIC
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