The emergence of the concept of a causal fermion system is revisited and further investigated for the vacuum Dirac equation in Minkowski space. After a brief recap of the Dirac equation and its solution space, in order to allow for the effects of a possibly nonstandard structure of spacetime at the Planck scale, a regularization by a smooth cutoff in momentum space is introduced, and its properties are discussed. Given an ensemble of solutions, we recall the construction of a local correlation function, which realizes spacetime in terms of operators. It is shown in various situations that the local correlation function maps spacetime points to operators of maximal rank and that it is closed and homeomorphic onto its image. It is inferred that the corresponding causal fermion systems are regular and have a smooth manifold structure. The cases considered include a Dirac sea vacuum and systems involving a finite number of particles and antiparticles.

重新讨论了因果费米子系统概念的出现，并进一步研究了Minkowski空间中真空Dirac方程。在简要回顾了Dirac方程及其解空间之后，为了考虑普朗克尺度上可能存在的时空结构的非标准结构的影响，引入了动量空间中平滑截止的正则化，并讨论了其性质。给定一组解决方案，我们回想起局部相关函数的构造，该函数可以根据算符实现时空。在各种情况下都表明，局部相关函数将时空点映射到最大秩的算子，并且它是封闭的且在其图像上是同胚的。可以推断，相应的因果费米子系统是规则的，并且具有光滑的歧管结构。