The Continuum Limit of Causal Fermion Systems

Abstract

This monograph introduces the basic concepts of the theory of causal fermion systems, a recent approach to the description of fundamental physics. The theory yields quantum mechanics, general relativity and quantum field theory as limiting cases and is therefore a candidate for a unified physical theory. From the mathematical perspective, causal fermion systems provide a general framework for describing and analyzing non-smooth geometries and "quantum geometries." The dynamics is described by a novel variational principle, called the causal action principle. In addition to the basics, the book provides all the necessary mathematical background and explains how the causal action principle gives rise to the interactions of the standard model plus gravity on the level of second-quantized fermionic fields coupled to classical bosonic fields. The focus is on getting a mathematically sound connection between causal fermion systems and physical systems in Minkowski space. The book is intended for graduate students entering the field, and is furthermore a valuable reference work for researchers in quantum field theory and quantum gravity.

457 pages, 11 figures, minor improvements

Cited by in corpus (25)

• Inextendibility of spacetimes and Lorentzian length spaces
• A Hamiltonian Formulation of Causal Variational Principles
• Causal Fermion Systems: An Elementary Introduction to Physical Ideas and Mathematical Concepts
• A review of Lorentzian synthetic theory of timelike Ricci curvature bounds
• Causal Fermion Systems: A Primer for Lorentzian Geometers
• Banach Manifold Structure and Infinite-Dimensional Analysis for Causal Fermion Systems
• Fermionic Fock Spaces and Quantum States for Causal Fermion Systems
• Two-Dimensional Area and Matter Flux in the Theory of Causal Fermion Systems
• A Class of Conserved Surface Layer Integrals for Causal Variational Principles
• Causal Variational Principles in the $\sigma$-Locally Compact Setting: Existence of Minimizers
• Causal Fermion Systems and the ETH Approach to Quantum Theory
• Singular Support of Minimizers of the Causal Variational Principle on the Sphere
• Causal Fermion Systems and Octonions
• On the Mathematical Foundations of Causal Fermion Systems in Minkowski Space
• A Notion of Entropy for Causal Fermion Systems
• The Fermionic Signature Operator and Hadamard States in the Presence of a Plane Electromagnetic Wave
• On the von Neumann rule in quantization
• Local Algebras for Causal Fermion Systems in Minkowski Space
• Notions of Fermionic Entropies of a Causal Fermion System
• The Homogeneous Causal Action Principle on a Compact Domain in Momentum Space
• Elliptic Methods for Solving the Linearized Field Equations of Causal Variational Principles
• Lectures on Linear Stability of Rotating Black Holes
• Linear Bosonic Quantum Field Theories Arising from Causal Variational Principles
• A Positive Quasilocal Mass for Causal Variational Principles
• Holographic Mixing and Fock Space Dynamics of Causal Fermion Systems