Causal Fermion Systems: A Quantum Space-Time Emerging from an Action Principle

TL;DR

This paper introduces causal fermion systems as a comprehensive framework for relativistic quantum theory, demonstrating how they can produce a quantum space-time with emergent topology, causal structure, and quantized discreteness.

Contribution

It develops the mathematical foundation of causal fermion systems, connecting them to existing notions and proposing a quantum geometry with emergent space-time structure.

Findings

Support of minimizers shows a quantization effect leading to space-time discreteness

Framework recovers known notions like fermionic projector and causal variational principles

Outlines construction of spin connection and curvature in quantum geometry

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.