因果费米系统、非交换几何与广义迹动力学
Causal Fermion Systems, Non-Commutative Geometry and Generalized Trace Dynamics
AI总结：
因果费米系统通过广义两点相关子编码时空点间关系，与非交换几何和广义迹动力学进行比较，揭示其在连续极限下恢复几何结构的核心创新。
摘要：
我们比较因果费米系统理论中的结构和方法与广义迹动力学和非交换几何中的结构和方法。尽管这三个理论在许多方面有所不同，但它们一致认为在连续极限下恢复的几何结构不是裸空间时间，而是一个合适的纤维丛。进一步的比较使我们得出结论，因果费米系统的关键创新在于不同时空点之间关系的编码方式。在曼尼福德中编码任意两点间测地距离的经典世界函数σ(x,y)的角色，由广义两点相关子所取代。我们展示了这一想法可以应用于非交换几何和广义迹动力学。
英文摘要：
We compare the structures and methods in the theory of causal fermion systems with generalized trace dynamics and non-commutative geometry. Although the three theories differ on many aspects, they agree in that the geometric structure to be recovered in the continuum limit is not the bare spacetime but a suitable fiber bundle. Furthermore, the comparison leads us to the conclusion that the key innovation in causal fermion systems lies in the manner in which the relation between different spacetime points is encoded. The role of Synge's classical world function $σ(x,y)$ that encodes the geodesic distance between any two points in the manifold, is taken by a generalized two-point correlator. We show that this idea can be transferred to non-commutative geometry and generalized trace dynamics.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
