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The Axiom of Choice in Quantum Theory
Author(s) -
Brunner Norbert,
Svozil Karl,
Baaz Matthias
Publication year - 1996
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/malq.19960420128
Subject(s) - mathematics , axiom of choice , hilbert space , axiom , counterexample , observable , eigenfunction , pure mathematics , zermelo–fraenkel set theory , operator (biology) , semigroup , quantum , algebra over a field , discrete mathematics , quantum mechanics , set theory , physics , computer science , set (abstract data type) , programming language , eigenvalues and eigenvectors , geometry , biochemistry , chemistry , repressor , transcription factor , gene
We 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.