共形协方差与分裂性质
Conformal covariance and the split property
摘要：
我们表明，对于一个共形的局部网的观察的圆，分裂属性是自动的。全共形协方差（即复同态协方差）和圆的设置在这一事实中起着重要的作用，而通过先前构建的例子，我们已经知道，即使在圆上，莫比乌斯协方差也不意味着分裂性质。另一方面，这里我们也提供了一个生活在二维闵可夫斯基空间上的局部共形网的例子，尽管它是复同态协变的，但它不具有分裂性质。
英文摘要：
We show that for a conformal local net of observables on the circle, the split property is automatic. Both full conformal covariance (i.e. diffeomorphism covariance) and the circle-setting play essential roles in this fact, while by previously constructed examples it was already known that even on the circle, Möbius covariance does not imply the split property. On the other hand, here we also provide an example of a local conformal net living on the two-dimensional Minkowski space, which - although being diffeomorphism covariant - does not have the split property.
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