International Journal of Theoretical Physics

, Volume 43, Issue 1, pp 265–298

Interpreting Observables in a Quantum World from the Categorial Standpoint

  • Elias Zafiris

DOI: 10.1023/B:IJTP.0000028863.07313.9c

Cite this article as:
Zafiris, E. International Journal of Theoretical Physics (2004) 43: 265. doi:10.1023/B:IJTP.0000028863.07313.9c


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.

Boolean quantum observables localization adjunction topos sheaves quantum logic abstract differential geometry 

Copyright information

© Plenum Publishing Corporation 2004

Authors and Affiliations

  • Elias Zafiris
    • 1
  1. 1.Faculty of Mathematics and InformaticsUniversity of SofiaSofiaBulgaria

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