# The Theory of Causal Fermion Systems

## Introductory Videos

These videos describe the content of corresponding websites. They are intended to give a nontechnical introduction and an impressionistic overview.

## Online Course on Causal Fermion Systems

The online course originates from online lectures given at Universität Regensburg in the summer term 2021. It includes introductory videos, more specialized lectures, exercises and many links to books and articles.

## Books

• F. Finster, N. Kamran, Spinors on Singular Spaces and the Topology of Causal Fermion Systems, Mem. Amer. Math. Soc. 259 (2019), no. 1251, v+83 pp
This thin book introduces causal fermion systems from the perspective of topology and differential geometry. The guiding theme is to encode the topology and geometry in terms of linear operators on a Hilbert space. This is explained and illustrated in many simple examples. The causal action principle, however, is not covered.
• F. Finster, The Continuum Limit of Causal Fermion Systems, Fundamental Theories of Physics 186, Springer, 2016
This is the only textbook on and at present the best reference to causal fermion systems. Chapter 1 is a general introduction. Chapter 2 provides the computational tools needed for analyzing the continuum limit. In Chapters 3-5 the continuum limit is worked out for Dirac systems of increasing complexity, giving all the interactions of the standard model plus classical gravity.
• F. Finster, The Principle of the Fermionic Projector, AMS/IP Studies in Advanced Mathematics Series 35 (2006)
The “principle of the fermionic projector” was a major preliminary step towards developing causal fermion systems. It states the general mathematical structure of the causal action principle in the setting where wave functions are varied in a discrete space-time. Moreover, the causal action is stated for the first time, but ony as an example and without all the constraints. In the more recent foreword, the developments leading to causal fermion systems are outlined.

## Lecture Notes

• F. Finster, S. Kindermann, J.-H. Treude, An Introductory Course on Causal Fermion Systems
This book draft is based on notes of lectures on causal variational principles given at the University of Regensburg in the spring terms 2017 and 2021. The intention is to address both physicists and mathematicians interested in the subject. Part 3 can be regarded as a mathematical toolbox which provides useful methods and techniques.

## Live Recordings of Talks at Conferences, Workshops and Seminars

Here are a few selected videos of talks given at conferences, workshops or seminars: