Causal Fermion Systems: Classical Gravity and Beyond

TL;DR

This paper reviews how causal fermion systems can reproduce classical gravity and Einstein equations, and explores extensions beyond classical gravity including quantum states and matter flux connections.

Contribution

It introduces methods to derive classical gravity from causal fermion systems and proposes approaches to extend beyond classical gravity.

Findings

Derivation of Einstein equations from causal action principle

Connection between area change and matter flux

Construction of a quantum state within the framework

Abstract

In this short review, we explain how and in which sense the causal action principle for causal fermion systems gives rise to classical gravity and the Einstein equations. Moreover, methods are presented for going beyond classical gravity, with applications to a positive mass theorem for static causal fermion systems, a connection between area change and matter flux and the construction of a quantum state.