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Causal Fermion Systems
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Title: Causal Fermion Systems Subtitle: An Introduction to Fundamental Structures, Methods and Applications Series: Cambridge Monographs on Mathematical Physics Author: Finster, Felix (Universitat Regensburg, Germany) / Kindermann, Sebastian (Comenius Gymnasium Deggendorf, Germany) / Treude, Jan-Hendrik (Universitat Konstanz, Germany) Publisher: Cambridge University Press ISBN: 9781009632621 Cover: HARDCOVER Date: 2025年10月 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. As the first comprehensive text on causal fermion systems, the book is an essential resource for anyone with an interest in novel approaches to fundamental physics Covers the foundational mathematical and physical aspects in detail to ensure the book is accessible to as broad an audience as possible Well suited as a companion to self-guided study and as a framework for courses in the subject, with exercises included in each chapter to support learning TABLE OF CONTENTS 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 最近チェックした商品
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