After reviewing the theory of "causal fermion systems" (CFS theory) and the "Events, Trees, and Histories Approach" to quantum theory (ETH approach), we compare some of the mathematical structures underlying these two general frameworks and discuss similarities and differences. For causal fermion systems, we introduce future algebras based on causal relations inherent to a causal fermion system. These algebras are analogous to the algebras previously introduced in the ETH approach. We then show that the spacetime points of a causal fermion system have properties similar to those of "events", as defined in the ETH approach. Our discussion is underpinned by a survey of results on causal fermion systems describing Minkowski space that show that an operator representing a spacetime point commutes with the algebra in its causal future, up to tiny corrections that depend on a regularization length.

中文翻译：

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因果费米子系统和ETH量子理论方法

在回顾了“因果费米子系统”的理论（CFS理论）和量子理论的“事件，树和历史方法”（ETH方法）之后，我们比较了这两个通用框架的一些数学结构并讨论了异同。对于因果费米子系统，我们根据因果费米子系统固有的因果关系介绍未来的代数。这些代数类似于先前在ETH方法中引入的代数。然后，我们证明了因果性费米子系统的时空点具有与ETH方法中定义的“事件”相似的属性。