Quantum logics with existence property

Journal Article · Sun Mar 31 23:00:00 EST 1991 · Foundations of Physics; (United States)

DOI:https://doi.org/10.1007/BF00733360· OSTI ID:5363318

Schindler, C ^[1]

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1. Univ. Bern (Switzerland)

A quantum logic ({sigma}-orthocomplete orthomodular poset L with a convex, unital, and separating set {Delta} of states) is said to have the existence property if the expectation functionals on lin({Delta}) associated with the bounded observables of L form a vector space. Classical quantum logics as well as the Hilbert space logics of traditional quantum mechanics have this property. The author shows that, if a quantum logic satisfies certain conditions in addition to having property E, then the number of its blocks (maximal classical subsystems) must either be one (classical logics) or uncountable (as in Hilbert space logics).

• OSTI ID: 5363318
• Journal Information: Foundations of Physics; (United States), Journal Name: Foundations of Physics; (United States) Vol. 21:4; ISSN 0015-9018; ISSN FNDPA
• Country of Publication: United States
• Language: English

Related Subjects

661100* -- Classical & Quantum Mechanics-- (1992-)
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ALGEBRA
BANACH SPACE
CLASSICAL MECHANICS
HILBERT SPACE
MATHEMATICAL LOGIC
MATHEMATICAL SPACE
MATHEMATICS
MECHANICS
PROBABILITY
QUANTUM MECHANICS
SPACE