Similarity-Projection Structures: The Logical Geometry of Quantum Physics
Similarity-Projection Structures: The Logical Geometry of Quantum Physics
复制标题
相似投影结构：量子物理的逻辑几何
DOI：
10.1007/s10773-008-9801-3
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发表时间：
2008
影响因子：
1.4
通讯作者：
D. Lehmann
中科院分区：
文献类型：
--
作者：
D. Lehmann
相似-投影结构抽象了希尔伯特空间中射线与投影的实标量积的数值性质，为量子物理提供了一个更通用的框架。它们的特点是具有直接的物理意义。它们提供了一个形式框架，包含了关于集合和子集的经典布尔逻辑和关于希尔伯特空间、闭子空间和投影的量子逻辑。它们阐明了相位因子的作用，而相位因子是量子物理学的核心。将自伴随算子的概念推广到sp -结构，提供了一个不需要线性代数的新概念。
Similarity-Projection structures abstract the numerical properties of real scalar product of rays and projections in Hilbert spaces to provide a more general framework for Quantum Physics. They are characterized by properties that possess direct physical meaning. They provide a formal framework that subsumes both classical Boolean logic concerned with sets and subsets and quantum logic concerned with Hilbert space, closed subspaces and projections. They shed light on the role of the phase factors that are central to Quantum Physics. The generalization of the notion of a self-adjoint operator to SP-structures provides a novel notion that is free of linear algebra.