论文标题
复杂顺序增长模型中协方差的标准
A Criterion for Covariance in Complex Sequential Growth Models
论文作者
论文摘要
因果集的经典顺序生长模型为深度量子制度中的动力学提供了模板。这种增长动态在本质上是时间和因果关系，每个新元素都将添加到现有的因果集合中，而不会扰乱其过去。在量子版本中，事件代数上的概率度量被量子度量取代，量子是希尔伯特空间值的。由于生长过程的时间性，在这种方法中，仅当量子测量扩展到事件的相关Sigma代数时，协变量可观察物（或Beables）才能测量。这并不总是保证。在这项工作中，我们找到了因果集的复杂顺序增长模型中扩展（以及协方差）的标准。我们发现了一个大型模型，该模型可以在其中扩展，因此所有协变量可观察物都是可衡量的。
The classical sequential growth model for causal sets provides a template for the dynamics in the deep quantum regime. This growth dynamics is intrinsically temporal and causal, with each new element being added to the existing causal set without disturbing its past. In the quantum version, the probability measure on the event algebra is replaced by a quantum measure, which is Hilbert space valued. Because of the temporality of the growth process, in this approach, covariant observables (or beables) are measurable only if the quantum measure extends to the associated sigma algebra of events. This is not always guaranteed. In this work we find a criterion for extension (and thence covariance) in complex sequential growth models for causal sets. We find a large family of models in which the measure extends, so that all covariant observables are measurable.
