Causal Fermion Systems

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.