Causal fermion systems: A quantum space-time emerging from an action principle

Abstract

Causal fermion systems are introduced as a general mathematical framework for formulating relativistic quantum theory. By specializing, we recover earlier
notions like fermion systems in discrete space-time, the fermionic projector and causal variational principles. We review how an effect of spontaneous structure formation
gives rise to a topology and a causal structure in space-time. Moreover, we outline how to construct a spin connection and curvature, leading to a proposal for a “quantum geometry” in the Lorentzian setting. We review recent numerical and analytical results on the support of minimizers of causal variational principles which reveal a “quantization effect” resulting in a discreteness of space-time. A brief survey is given on the correspondence to quantum field theory and gauge theories.