凸与序列效应代数
Convex and Sequential Effect Algebras
摘要：
我们提出了一个量子力学的数学框架，其中的基本实体和操作具有物理意义。在这个框架中的原始概念是状态和效果，由此产生的数学结构是一个凸效果代数。我们刻画了经典的凸效应代数和量子力学的凸效应代数。量子力学的是那些可以在复希尔伯特空间上表示的。接下来，我们引入效应的序列积来形成凸序列效应代数。这个产品使得研究条件概率和期望成为可能。
英文摘要：
We present a mathematical framework for quantum mechanics in which the basic entities and operations have physical significance. In this framework the primitive concepts are states and effects and the resulting mathematical structure is a convex effect algebra. We characterize the convex effect algebras that are classical and those that are quantum mechanical. The quantum mechanical ones are those that can be represented on a complex Hilbert space. We next introduce the sequential product of effects to form a convex sequential effect algebra. This product makes it possible to study conditional probabilities and expectations.
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。
