Causal Fermion Systems
An Introduction to Fundamental Structures, Methods and Applications
Published on 23. October 2025
Book
Hardback
412 pages
978-1-009-63262-1 (ISBN)
Description
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.
More details
Series
Language
English
Place of publication
Cambridge
United Kingdom
Target group
College/higher education
Illustrations
Worked examples or Exercises
Dimensions
Height: 250 mm
Width: 175 mm
Thickness: 27 mm
Weight
907 gr
ISBN-13
978-1-009-63262-1 (9781009632621)
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Schweitzer Classification
Persons
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.
Content
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.