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The theory of causal fermion systems is a new physical theory which aims todescribe a fundamental level of physical reality. Its mathematical core is thecausal action principle. In this thesis, we develop a formalism which connectsthe causal action principle to a suitable notion of fields on space-time. Wederive field equations from the causal action principle and find that thedynamics induced by the field equations conserve a symplectic form which givesrise to an Hamiltonian time evolution if the causal fermion system admits anotion of time. In this way, we establish the dynamics of causal fermionsystems. Remarkably, the causal action principle implies that there arecorrection terms to the field equations, which we subsequently derive andstudy. In particular, we prove that there is a stochastic and a non-linearcorrection term and investigate how they relate to the Hamiltonian timeevolution. Furthermore, we give theorems which generalize the connectionbetween symmetries and conservation laws in Noether's theorems to the theory ofcausal fermion systems. The appearance of the particular correction terms isreminiscent of dynamical collapse models in quantum theory.

Dynamics of Causal Fermion Systems. Field Equations and Correction Terms for a New Unified Physical Theory