标题： 因果费米子系统和八元数 显示英文标题

标题： Causal Fermion Systems and Octonions

摘要： 我们比较了因果费米子系统理论中的结构和方法与基于除法代数的基本物理方法，特别是八元数。 我们发现八元数以及更一般地，除法代数的张量积自然地用于描述因果费米子系统真空配置的对称性。 这是通过将实部和虚部八元数基底元素分别与真空费米子投影算子的中微子和带电部分相关联来实现的。 相反，因果费米子系统通过因果作用原理为八元数理论提供了时空结构和动力学方程。 这样，八元数理论和因果费米子系统相互补充。 显示英文摘要

摘要： We compare the structures and methods in the theory of causal fermion systems with approaches to fundamental physics based on division algebras, in particular the octonions. We find that octonions and, more generally, tensor products of division algebras come up naturally to describe the symmetries of the vacuum configuration of a causal fermion system. This is achieved by associating the real and imaginary octonion basis elements with the neutrino and charged sectors of the vacuum fermionic projector, respectively. Conversely, causal fermion systems provide octonionic theories with spacetime structures and dynamical equations via the causal action principle. In this way, octonionic theories and causal fermion systems complement each other..