• Home
  • Theory
    • Mathematics
      • Basic definitions
      • Generalizations and special cases
      • Existence theory
      • Spin spaces and physical wave functions
      • The fermionic projector
      • Geometric structures
      • Surface layer integrals
      • The Euler-Lagrange equations
      • The linearized field equations
      • The dynamical wave equation
      • Construction of linear fields and waves
      • Minkowski space as a causal fermion system
      • The continuum limit
      • Connection to quantum field theory
      • Connection to General Relativity
      • Manifolds of operators
      • Operator algebras
      • Causal cone structures
      • Fock space structures
      • Notions of entropy
      • Positive functionals
      • The fermionic signature operator
      • Action-driven flows
    • Physics
      • What is a causal fermion system?
      • The causal structure
      • Motivation for the choice of F
      • The causal action principle
      • The continuum limit
      • The logic underlying the derivation of the classical field equations
      • The Standard Model and General Relativity
      • Quantum field theory
      • Why the Dirac sea?
      • What is fundamental?
      • Underlying physical principles
      • A mechanism of baryogenesis
      • A mechanism for dark matter and dark energy
      • Comments on Quantum Gravity wishlists
      • Extended explanation of physical aspects
      • Relation to other theories
      • Frequently asked questions

    Mathematics

    Basics

    • Basic definitions
    • Generalizations and special cases
    • Existence theory

    Examples and Limiting Cases

    • Minkowski space as a causal fermion system
    • The continuum limit
    • Connection to quantum field theory
    • Connection to General Relativity

    Inherent Structures

    • Spin spaces and physical wave functions
    • The fermionic projector
    • Geometric structures
    • Surface layer integrals

    Further Structures I

    • Manifolds of operators
    • Operator algebras
    • Causal cone structures
    • Fock space structures
    • Notions of entropy

    Analytic Structures

    • The Euler-Lagrange equations
    • The linearized field equations
    • The dynamical wave equation
    • Construction of linear fields and waves

    Further Structures II

    • Positive functionals
    • The fermionic signature operator
    • Action-driven flows

    Physics

    Motivation in Examples

    Elementary Structures

    • What is a causal fermion system?
    • The causal structure
    • Motivation for the choice of $\F$

    Phenomenology

    • A mechanism of baryogenesis
    • A mechanism for dark matter and dark energy
    • Wave function collapse

    Central Ideas of the Theory

    • The causal action principle
    • The continuum limit
    • The logic underlying the derivation of the classical field equations

    Wishlists and Relation to Other Theories

    • Comments on various quantum gravity wishlists
    • Relation to other theories

    Main Results and Ontology

    • The Standard Model and General Relativity
    • Quantum field theory
    • Why the Dirac sea?
    • What is fundamental?
    • Underlying physical principles

    FAQ

  • Learning
    Introductory videos
    Online course
    Literature
    Further videos
  • Research
    • Current research projects
    • Future perspectives
    Current research projects
    Future perspectives
  • Community
  • Events
    • Regular events
    • Causal Fermion Systems 2025
    Regular events
    Causal Fermion Systems 2025
  • Internal
  • Home
  • Mathematics
    ▼
    • Basic definitions
    • Generalizations and special cases
    • Existence theory
    • Spin spaces and physical wave functions
    • The fermionic projector
    • Geometric structures
    • Surface layer integrals
    • The Euler-Lagrange equations
    • The linearized field equations
    • The dynamical wave equation
    • Construction of linear fields and waves
    • Minkowski space as a causal fermion system
    • The continuum limit
    • Connection to quantum field theory
    • Connection to General Relativity
    • Manifolds of operators
    • Operator algebras
    • Causal cone structures
    • Fock space structures
    • Notions of entropy
    • Positive functionals
    • The fermionic signature operator
    • Action-driven flows
  • Physics
    ▼
    • Motivation in examples
    • What is a causal fermion system?
    • The causal structure
    • Motivation for the choice of F
    • The causal action principle
    • The continuum limit
    • The logic underlying the derivation of the classical field equations
    • The Standard Model and General Relativity
    • Quantum field theory
    • Why the Dirac sea?
    • What is fundamental?
    • Underlying physical principles
    • A mechanism of baryogenesis
    • A mechanism for dark matter and dark energy
    • Wave function collapse
    • Comments on Quantum Gravity wishlists
    • Extended explanation of physical aspects
    • Relation to other theories
  • Learning
  • Research
    ▼
    • Current research projects
    • Future perspectives
  • Community
  • Events
    ▼
    • Regular events
    • Causal Fermion Systems 2025
  • Internal
  • FAQ