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

Felix Finster; Sebastian Kindermann; Jan‐Hendrik Treude

doi:10.1017/9781009632638

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.

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Contents

Frontmatter
pp i-vi
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Contents
pp vii-xii
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Preface
pp xiii-xiv
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How to Use This Book
pp xv-xvi
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Part I - Physical and Mathematical Background
pp 1-2
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1 - Physical Preliminaries
pp 3-20
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2 - Mathematical Preliminaries
pp 21-58
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3 - Elements of Operator Theory
pp 59-67
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4 - Spinors in Curved Spacetime
pp 68-90
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Part II - Causal Fermion Systems: Fundamental Structures
pp 91-92
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5 - A Brief Introduction to Causal Fermion Systems
pp 93-134
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6 - Causal Variational Principles
pp 135-147
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7 - The Euler–Lagrange Equations
pp 148-155
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8 - The Linearized Field Equations
pp 156-170
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9 - Surface Layer Integrals and Conservation Laws
pp 171-189
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10 - Positive Functionals
pp 190-198
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11 - Topological and Geometric Structures
pp 199-212
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Part III - Mathematical Methods and Analytic Constructions
pp 213-214
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12 - Measure-Theoretic Methods
pp 215-242
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13 - Methods of Hyperbolic Partial Differential Equations
pp 243-267
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14 - Energy Methods for the Linearized Field Equations
pp 268-278
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15 - Functional Analytic Methods in Spacetime
pp 279-295
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16 - Fourier Methods
pp 296-308
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17 - Methods of Scattering Theory
pp 309-319
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18 - Methods of Perturbation Theory
pp 320-327
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19 - Methods of Microlocal Analysis
pp 328-350
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Part IV - Applications and Outlook
pp 351-352
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20 - A Few Explicit Examples of Causal Variational Principles
pp 353-365
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21 - Basics on the Continuum Limit
pp 366-378
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22 - Connection to Quantum Field Theory
pp 379-387
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Causal Fermion Systems

An Introduction to Fundamental Structures, Methods and Applications

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