论文标题
因果效率系统的动力学。新的统一物理理论的现场方程和更正术语
Dynamics of Causal Fermion Systems. Field Equations and Correction Terms for a New Unified Physical Theory
论文作者
论文摘要
因果关系系统的理论是一种新的物理理论，旨在描述物理现实的基本水平。它的数学核心是因果行动原理。在本论文中，我们开发了一种形式主义，该形式主义将因果行动原理与时空上的适当概念联系起来。我们从因果行动原理中得出场方程，并发现磁场方程诱导的动力学保留了符号形式，如果因果关系系统允许时间概念，则会导致汉密尔顿时间的演变。通过这种方式，我们建立了因果费系统的动力学。值得注意的是，因果行动原理意味着我们随后得出和研究的场方程有校正术语。特别是，我们证明存在一个随机性和非线性校正项，并研究了它们与哈密顿时间演化的关系。此外，我们给出了定理，该定理概括了Noether定理中对称性和保护定律与因果关系理论的联系。特定校正项的外观让人联想到量子理论中动态塌陷模型。
The theory of causal fermion systems is a new physical theory which aims to describe a fundamental level of physical reality. Its mathematical core is the causal action principle. In this thesis, we develop a formalism which connects the causal action principle to a suitable notion of fields on space-time. We derive field equations from the causal action principle and find that the dynamics induced by the field equations conserve a symplectic form which gives rise to an Hamiltonian time evolution if the causal fermion system admits a notion of time. In this way, we establish the dynamics of causal fermion systems. Remarkably, the causal action principle implies that there are correction terms to the field equations, which we subsequently derive and study. In particular, we prove that there is a stochastic and a non-linear correction term and investigate how they relate to the Hamiltonian time evolution. Furthermore, we give theorems which generalize the connection between symmetries and conservation laws in Noether's theorems to the theory of causal fermion systems. The appearance of the particular correction terms is reminiscent of dynamical collapse models in quantum theory.
