希尔伯特空间效应代数的余性及其对称变换的一个刻画
Coexistency on Hilbert space effect algebras and a characterisation of its symmetry transformations
摘要：
希尔伯特空间效应代数是路德维希量子力学公式中用来描述非尖锐量子测量的基本数学结构。每个效应代表一个量子（模糊）事件。共存关系在这个理论中起着重要的作用，因为它表达了两个量子事件何时可以通过应用合适的仪器一起测量。本文的第一个目标是回答一个非常自然的问题，这种关系，即，当两个效果是完全相同的效果共存？另一个主要目的是描述关于共存关系的效应代数的所有自同构。特别是，我们将看到它们可以与通常的标准自同构有很大的不同，例如在路德维希定理中出现的自同构。作为我们的方法的副产品，我们还加强了莫尔纳定理。
英文摘要：
The Hilbert space effect algebra is a fundamental mathematical structure which is used to describe unsharp quantum measurements in Ludwig's formulation of quantum mechanics. Each effect represents a quantum (fuzzy) event. The relation of coexistence plays an important role in this theory, as it expresses when two quantum events can be measured together by applying a suitable apparatus. This paper's first goal is to answer a very natural question about this relation, namely, when two effects are coexistent with exactly the same effects? The other main aim is to describe all automorphisms of the effect algebra with respect to the relation of coexistence. In particular, we will see that they can differ quite a lot from usual standard automorphisms, which appear for instance in Ludwig's theorem. As a byproduct of our methods we also strengthen a theorem of Molnar.
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。
