大型玩具模型：将物理系统表示为Chu空间
Big Toy Models: Representing Physical Systems As Chu Spaces
摘要：
我们追求一种面向模型而不是公理化的方法来理解量子力学的基础，我们的想法是新的模型往往可以提出新的公理。这种方法在逻辑和理论计算机科学中经常是富有成效的。我们的目标不是建立一个简化的玩具模型，而是建立一个“大玩具模型”，在这个模型中，量子和经典系统都可以被忠实地表示出来--也可能是更奇异的系统。为此，我们展示了如何楚空间可以用来表示各种物理系统。特别是，我们展示了量子系统如何可以表示为在单位间隔上的Chu空间，以这样一种方式，Chu态射完全对应于系统的物理意义的对称性-幺正和反幺正。这样，我们就从Hilbert空间的广群及其对称性到Chu空间得到了一个完整的忠实函子。我们还考虑是否有可能使用一个有限的值集，而不是单位区间，我们表明，三个值就足够了，而两个标准的可能性减少到两个值都未能保持丰满。
英文摘要：
We pursue a model-oriented rather than axiomatic approach to the foundations of Quantum Mechanics, with the idea that new models can often suggest new axioms. This approach has often been fruitful in Logic and Theoretical Computer Science. Rather than seeking to construct a simplified toy model, we aim for a `big toy model', in which both quantum and classical systems can be faithfully represented - as well as, possibly, more exotic kinds of systems. To this end, we show how Chu spaces can be used to represent physical systems of various kinds. In particular, we show how quantum systems can be represented as Chu spaces over the unit interval in such a way that the Chu morphisms correspond exactly to the physically meaningful symmetries of the systems - the unitaries and antiunitaries. In this way we obtain a full and faithful functor from the groupoid of Hilbert spaces and their symmetries to Chu spaces. We also consider whether it is possible to use a finite value set rather than the unit interval; we show that three values suffice, while the two standard possibilistic reductions to two values both fail to preserve fullness.
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