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Mathematical Logic Quarterly
Article . 1996 . Peer-reviewed
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The Axiom of Choice in Quantum Theory

The axiom of choice in quantum theory
descriptionPublicationkeyboard_double_arrow_right Article 01 Jan 1996 English Publisher:WileyJournal:Mathematical Logic Quarterly, volume 42, pages 319-340 (issn: 0942-5616, eissn: 1521-3870, Copyright policy )
Authors: Brunner, Norbert; Svozil, Karl; Baaz, Matthias;

doi: 10.1002/malq.19960420128

The Axiom of Choice in Quantum Theory

Abstract

AbstractWe construct peculiar Hilbert spaces from counterexamples to the axiom of choice. We identify the intrinsically effective Hamiltonians with those observables of quantum theory which may coexist with such spaces. Here a self adjoint operator is intrinsically effective if and only if the Schrödinger equation of its generated semigroup is soluble by means of eigenfunction series expansions.Mathematics Subject Classification: 03E35, 81P10, 03E25, 35Q40, 46B26, 47A60.

Related Organizations
Keywords

Functional calculus for linear operators, Hilbert spaces, Nonseparable Banach spaces, Axiom of choice and related propositions, linear self-adjoint operators, Axiom of Choice, Fock space, quantum observables, quantum dynamics, Logical foundations of quantum mechanics; quantum logic (quantum-theoretic aspects), Consistency and independence results, PDEs in connection with quantum mechanics

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
4
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