量子可观测量范畴的拓扑理论参考系
Topos Theoretical Reference Frames on the Category of Quantum Observables
摘要：
一个可观测的影响，通过相关的布尔代数挑选测量与波莱尔代数的实数线的量子事件结构的图式。在一个定义明确的意义上，布尔可观测量在量子世界中扮演着协调对象的角色，通过挑选布尔图形并随后打开布尔窗口来感知后者，解释为局部测量图表。基于范畴论方法，本文提出了实现本论文的数学方案。该方案导致一个流形表示的量子结构的拓扑理论布尔参考系。协调对象产生的结构保持映射的建模对象作为其域，最终影响量子事件代数对象和布尔本地化系统的测量的可观测量之间的同构。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
