Interpreting Observables in a Quantum World from the Categorial Standpoint
- Elias Zafiris
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We develop a relativistic perspective on structures of quantum observables, in terms of localization systems of Boolean coordinatizing charts. This perspective implies that the quantum world is comprehended via Boolean reference frames for measurement of observables, pasted together along their overlaps. The scheme is formalized categorically, as an instance of the adjunction concept. The latter is used as a framework for the specification of a categorical equivalence signifying an invariance in the translational code of communication between Boolean localizing contexts and quantum systems. Aspects of the scheme semantics are discussed in relation to logic. The interpretation of coordinatizing localization systems, as structure sheaves, provides the basis for the development of an algebraic differential geometric machinery suited to the quantum regime.
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- Interpreting Observables in a Quantum World from the Categorial Standpoint
International Journal of Theoretical Physics
Volume 43, Issue 1 , pp 265-298
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- Kluwer Academic Publishers-Plenum Publishers
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- quantum logic
- abstract differential geometry
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- Elias Zafiris (1)
- Author Affiliations
- 1. Faculty of Mathematics and Informatics, University of Sofia, Blvd. James Bourchier, Sofia, Bulgaria