The Theory of Causal Fermion Systems

Overview of Physical Aspects

In what follows, we explain the mathematical framework underlying causal fermion systems. This page is set up in a “build your own adventure” style. Every subpage explains one concept. At the top of the page you will find a list of pages which we recommend to have read before the one you are looking at, and in the end you find a list with further readings. The explanations in this section are geared more towards a physics audience and therefore mathematical rigor was not top priority. If you prefer a more rigorous approach, you can find here an explanation focusing on the mathematical aspects. 
Below we give an overview of the subpages and how they are connected. On every page the list of prerequisites indicate which subpages you should have read before you start with this particular topic.
If you are interested in open physical questions, you may find it helpful to check out the collection of Quantum Gravity wish lists and our comments what the theory of Causal Fermion Systems has to say about them. Nevertheless, we recommend reading through the extended explanation first. 

The Elementary Structures

Here you can find an introduction to the elementary structures of the theory and their basic properties.

What is a Causal Fermion System?

Here you find an introduction to the basic mathematical structures that make up a Causal Fermion System.

Causal Structure

Here we explain how a pointwise causal relation can be defined.

Motivation for F

On this page we give a motivation for the choice of the particular subspace of linear operators in the definition of a CFS.

The Central Ideas of the Theory

Here you find an introduction to the main ideas of the theory. First and foremost, the causal action principle which forms the core of the theory.

Causal Action Principle

The Causal Action Principle lies at the heart of the CFS theory.

The Continuum Limit

The continuum limit is the workhorse behind the derivation of the well established theories.

The Logic underlying the Derivation of the Classical Field Equations

As the derivation of physical laws in the CFS theory is different from most other theories, we dedicate this page to explain the logic at work.

Main Results and Ontology

Here we give an overview of the main results of the theory . We also discuss the physical motivation and interpretation of the theory.

The Standard Model and General Relativity

On this page we summarize the central physical results obtained so far in the theory of causal fermion systems.

Quantum Field Theory

In a well-defined limiting case, causal fermion systems give rise to quantum field theory. We here summarize the present status and open problems.

Why the Dirac Sea?

The original conception of the theory of causal fermion systems took the Dirac Sea as a starting point. Here we explain the motivation for this starting point.

What is fundamental?

Here we address the question which concepts are fundamental and which are emergent phenomena.

Underlying physical principles

Here we discuss which physical principles are built in or respected by theory of causal fermion systems.


The theory of causal fermion systems aims at making physical predictions. Here are first steps in this direction.

A Mechanism of Baryogenesis

The theory of causal fermion systems gives rise to a novel mechanism giving rise to a particle/anti-particle asymmetry and the creation of matter.

A Mechanism for Dark Matter and Dark Energy

The theory of causal fermion systems gives a possible explanation for dark matter and dark energy.

Wave function collapse

Causal fermion systems gives rise to an effective collapse theory.

Wishlists and Relation to Other Theories

Here you find an overview of which open questions in fundamental theoretical physics are addressed by the Theory of Causal Fermion Systems and how the approach relates to other theories.

Comments on Quantum Gravity Wishlists

On this page we present a collection of quantum gravity wishlists by various people and comment on what the CFS theory has to say about them.

Relation to other Theories

Here we explore what sets CFS apart from other approaches to unification/quantum Gravity.