序单位空间中量子测量的一种表示
A Representation of Quantum Measurement in Order-Unit Spaces
摘要：
考虑了算子代数以外的量子力学数学形式的某种推广。该方法基于条件概率的概念和作为概率条件化规则的Lueders-von Neumann量子测量的解释。一个重要结果表明，在推广的方法中，算子代数必须用具有某些特殊性质的序单位空间来代替，并分析了在什么条件下这些序单位空间成为Jordan代数.这个结果的一个应用提供了算子代数中投影格的一个刻画。
英文摘要：
A certain generalization of the mathematical formalism of quantum mechanics beyond operator algebras is considered. The approach is based on the concept of conditional probability and the interpretation of the Lueders - von Neumann quantum measurement as a probability conditionalization rule. A major result shows that the operator algebras must be replaced by order-unit spaces with some specific properties in the generalized approach, and it is analyzed under which conditions these order-unit spaces become Jordan algebras. An application of this result provides a characterization of the projection lattices in operator algebras.
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