Sheaf-theoretic representation of quantum measure algebras

Journal Article · Fri Sep 15 00:00:00 EDT 2006 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.2337848· OSTI ID:20860886

Zafiris, Elias ^[1]

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1. University of Athens, Institute of Mathematics, Panepistimiopolis, 15784 Athens (Greece)

We construct a sheaf-theoretic representation of quantum probabilistic structures, in terms of covering systems of Boolean measure algebras. These systems coordinatize quantum states by means of Boolean coefficients, interpreted as Boolean localization measures. The representation is based on the existence of a pair of adjoint functors between the category of presheaves of Boolean measure algebras and the category of quantum measure algebras. The sheaf-theoretic semantic transition of quantum structures shifts their physical significance from the orthoposet axiomatization at the level of events, to the sheaf-theoretic gluing conditions at the level of Boolean localization systems.

• OSTI ID: 20860886
• Journal Information: Journal of Mathematical Physics, Vol. 47, Issue 9; Other Information: DOI: 10.1063/1.2337848; (c) 2006 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ALGEBRA
MATHEMATICAL LOGIC
MEASURE THEORY
PROBABILISTIC ESTIMATION
QUANTUM MECHANICS