|
| related topics |
| {observables, space, algebra} |
| {measurement, state, measurements} |
| {group, space, representation} |
|
Topos Theoretical Reference Frames on the Category of Quantum Observables
Elias Zafiris
abstract: An observable effects a schematization of the Quantum event structure by
correlating Boolean algebras picked by measurements with the Borel algebra of
the real line. In a well-defined sense Boolean observables play the role of
coordinatizing objects in the Quantum world, by picking Boolean figures and
subsequently opening Boolean windows for the perception of the latter,
interpreted as local measurement charts. A mathematical scheme for the
implementation of this thesis is being proposed based on Category theoretical
methods. The scheme leads to a manifold representation of Quantum structure in
terms of topos-theoretical Boolean reference frames. The coordinatizing objects
give rise to structure preserving maps with the modeling objects as their
domains, effecting finally an isomorphism between quantum event algebra objects
and Boolean localization systems for the masurement of observables.
- oai_identifier:
- oai:arXiv.org:quant-ph/0202057
- categories:
- quant-ph
- comments:
- 39 pages, Latex
- arxiv_id:
- quant-ph/0202057
- created:
- 2002-02-11
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