The Theory of Causal Fermion Systems


Literature on causal fermion systems

Introductory and survey articles


  • 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: Part 1, Part 2, Appendices, 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, J. Kleiner, J.-H. Treude, An Introduction to the Fermionic Projector and 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 term 2016. The intention is to address both physicists and mathematicians interested in the subject. Part 3 can be regarded as a mathematical toolbox which provides the necessary methods and techniques.

Introductory talks for mathematicians in DFG research training network, 2016

Public talks and discussions

Live recordings of talks at conferences and workshops

Unfortunately, at most workshops and conferences no videos are taken. This is why only very few recordings are available: