A criterion for covariance in complex sequential growth models
A criterion for covariance in complex sequential growth models
复制标题
复杂序贯增长模型中协方差的标准
DOI：
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发表时间：
2020
影响因子：
3.5
通讯作者：
S. Zalel
中科院分区：
文献类型：
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作者：
S. Surya;S. Zalel
因果集的经典序列增长模型为深度量子体系中的动力学提供了一个模板。这种增长动态本质上是暂时的和因果的，每一个新元素都被添加到现有的因果集中，而不干扰它的过去。在量子版本中，事件代数上的概率测度被希尔伯特空间值的量子测度所取代。由于生长过程的时效性，在这种方法中，只有当量子测量扩展到事件的相关西格玛代数时，协变事件（或可观测事件）才可测量。这并不总是有保证的。在这项工作中，我们在因果集的复杂顺序增长模型中找到了一个扩展（以及协方差）的标准。我们发现了一个大的模型家族，其中的测量扩展，所以所有协变事件/可观察的是可测量的。
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 events (or observables) 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 events/observables are measurable.