Causal Fermion Systems: An Introduction to Fundamental Structures, Methods and Applications

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Felix Finster (Universität Regensburg, Germany) Sebastian Kindermann (Comenius Gymnasium Deggendorf, Germany)

Causal Fermion Systems

An Introduction to Fundamental Structures, Methods and Applications

Felix Finster (Universität Regensburg, Germany), Sebastian Kindermann (Comenius Gymnasium Deggendorf, Germany), Jan‐Hendrik Treude (Universität Konstanz, Germany)

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English

Cambridge University Press
23 October 2025

Cosmology & the universe; Particle & high-energy physics; Mathematical physics

Series: Cambridge Monographs on Mathematical Physics

The theory of causal fermion systems represents a novel approach to fundamental physics and is a promising candidate for a unified physical theory. This book offers a comprehensive overview of the theory, structured in four parts: the first lays the necessary mathematical and physical foundations; the second offers an introduction to the theory and the causal action principle; the third describes the mathematical tools for analyzing causal fermion systems; and the fourth gives an outlook on the key physical applications. With relevance across mathematical and theoretical physics, the book is aimed at graduate students and researchers interested in novel approaches to the structure of spacetime and alternative perspectives to the more established quantum field theories. It can be used for advanced courses in the subject or as a reference for research and self-guided study. Exercises are included at the end of each chapter to build and develop key concepts.

By: Felix Finster (Universität Regensburg Germany), Sebastian Kindermann (Comenius Gymnasium Deggendorf, Germany), Jan‐Hendrik Treude (Universität Konstanz, Germany)
Imprint: Cambridge University Press
Country of Publication: United Kingdom
Weight: 945g
ISBN: 9781009632621
ISBN 10: 1009632620
Series: Cambridge Monographs on Mathematical Physics
Pages: 412
Publication Date: 23 October 2025
Audience: College/higher education , Further / Higher Education
Format: Hardback
Publisher's Status: Active

How to use this book; Part I. Physical and Mathematical Background: 1. Physical preliminaries; 2. Mathematical preliminaries; 3. Elements of operator theory; 4. Spinors in curved spacetime; Part II. Causal Fermion Systems: Fundamental Structures: 5. A brief introduction to causal fermion systems; 6. Causal variational principles; 7. The Euler-Lagrange equations; 8. The linearized field equations; 9. Surface layer integrals and conservation laws; 10. Positive functionals; 11. Topological and geometric structures; Part III. Mathematical Methods and Analytic Constructions: 12. Measure-theoretic methods; 13. Methods of hyperbolic partial differential equations; 14. Energy methods for the linearized field equations; 15. Functional analytic methods in spacetime; 16. Fourier methods; 17. Methods of scattering theory; 18. Methods of perturbation theory; 19. Methods of microlocal analysis; Part IV. Applications and Outlook: 20. A few explicit examples of causal variational principles; 21. Basics on the continuum limit; 22. Connection to quantum field theory; Appendix. The spin coefficients; References; Notation index – in order of appearance; Notation index – thematic order; Subject index.

Felix Finster is Full Professor of Mathematics at the University of Regensburg. Following postdoctoral research at Harvard University, he was a member of the Max Planck Institute for Mathematics in the Sciences in Leipzig for four years. He has been at the University of Regensburg since 2002 and works on general relativity and quantum field theory. Sebastian Kindermann is currently a teacher at the Comenius Gymnasium in Deggendorf, Germany. He studied physics and mathematics at the University of Regensburg, completing his master's degree in 2020.