关于抽象H*-代数的结构

CoRR Pub Date : 2018-02-27 DOI:10.4204/EPTCS.266.13
Kevin Dunne
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引用次数: 1

摘要

以前我们已经证明,Doering和Isham的量子理论的拓扑方法可以推广到一类通常在Abramsky和Coecke的量子理论的一元方法中研究的范畴。在量子理论的一元方法中,H*-代数提供了状态和可观测物的公理化。在这里,我们证明了H*代数自然地与量子理论的广义拓扑方法中的状态和可观测值的概念相对应。然后,我们将这些结果与Heunen和Jacobs的量子逻辑的匕首核方法结合起来,我们使用它来证明H*-代数的结构定理。这个结构定理是Hilbert空间范畴H*-代数的Ambrose结构定理的推广。
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On the Structure of Abstract H*-Algebras
Previously we have shown that the topos approach to quantum theory of Doering and Isham can be generalised to a class of categories typically studied within the monoidal approach to quantum theory of Abramsky and Coecke. In the monoidal approach to quantum theory H*-algebras provide an axiomatisation of states and observables. Here we show that H*-algebras naturally correspond with the notions of states and observables in the generalised topos approach to quantum theory. We then combine these results with the dagger-kernel approach to quantumlogic of Heunen and Jacobs, which we use to prove a structure theorem for H*-algebras. This structure theorem is a generalisation of the structure theorem of Ambrose for H*-algebras the category of Hilbert spaces.
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