Boolean Coverings of Quantum Observable Structure: A Setting for an Abstract Differential Geometric Mechanism

Details Boolean Coverings of Quantum Observable Structure: A Setting for an Abstract Differential Geometric Mechanism Boolean Coverings of Quantum Observable Structure: A Setting for an Abstract Differential Geometric Mechanism

2003-06-16

arxiv.org/abs/math-ph/0306045v1

Physics

Mathematical Physics

25 pages, Latex

Scientific paper

10.1016/j.geomphys.2003.11.010

We develop the idea of employing localization systems of Boolean coverings, associated with measurement situations, in order to comprehend structures of Quantum Observables. In this manner, Boolean domain observables constitute structure sheaves of coordinatization coefficients in the attempt to probe the Quantum world. Interpretational aspects of the proposed scheme are discussed with respect to a functorial formulation of information exchange, as well as, quantum logical considerations. Finally, the sheaf theoretical construction suggests an opearationally intuitive method to develop differential geometric concepts in the quantum regime.

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