Causal Fermion Systems: A Quantum Space-Time Emerging from an Action Principle

Abstract

Causal fermion systems are introduced as a general mathematical framework for formulating relativistic quantum theory. By specializing, we recover earlier notions like fermion systems in discrete space-time, the fermionic projector and causal variational principles. We review how an effect of spontaneous structure formation gives rise to a topology and a causal structure in space-time. Moreover, we outline how to construct a spin connection and curvature, leading to a proposal for a "quantum geometry" in the Lorentzian setting. We review recent numerical and analytical results on the support of minimizers of causal variational principles which reveal a "quantization effect" resulting in a discreteness of space-time. A brief survey is given on the correspondence to quantum field theory and gauge theories.

23 pages, LaTeX, 2 figures, footnote added on page 9

References in corpus (11)

• A Lorentzian Quantum Geometry
• A Non-Perturbative Construction of the Fermionic Projector on Globally Hyperbolic Manifolds I - Space-Times of Finite Lifetime
• On the Support of Minimizers of Causal Variational Principles
• A Non-Perturbative Construction of the Fermionic Projector on Globally Hyperbolic Manifolds II -- Space-Times of Infinite Lifetime
• On the Structure of Minimizers of Causal Variational Principles in the Non-Compact and Equivariant Settings
• Perturbative Description of the Fermionic Projector: Normalization, Causality and Furry's Theorem
• Causal Variational Principles on Measure Spaces
• A Formulation of Quantum Field Theory Realizing a Sea of Interacting Dirac Particles
• Entanglement and Second Quantization in the Framework of the Fermionic Projector
• The Fermionic Projector, Entanglement, and the Collapse of the Wave Function
• An Action Principle for an Interacting Fermion System and its Analysis in the Continuum Limit

Cited by in corpus (24)

• A Lorentzian Quantum Geometry
• A Non-Perturbative Construction of the Fermionic Projector on Globally Hyperbolic Manifolds I - Space-Times of Finite Lifetime
• A Hamiltonian Formulation of Causal Variational Principles
• The Fermionic Projector in a Time-Dependent External Potential: Mass Oscillation Property and Hadamard States
• On the Support of Minimizers of Causal Variational Principles
• Causal Fermion Systems: An Elementary Introduction to Physical Ideas and Mathematical Concepts
• A Non-Perturbative Construction of the Fermionic Projector on Globally Hyperbolic Manifolds II -- Space-Times of Infinite Lifetime
• On the Structure of Minimizers of Causal Variational Principles in the Non-Compact and Equivariant Settings
• Causal Fermion Systems: A Primer for Lorentzian Geometers
• Perturbative Quantum Field Theory in the Framework of the Fermionic Projector
• Perturbative Description of the Fermionic Projector: Normalization, Causality and Furry's Theorem
• Spinors on Singular Spaces and the Topology of Causal Fermion Systems
• The Fermionic Projector, Entanglement, and the Collapse of the Wave Function
• Causal Fermion Systems: Discrete Space-Times, Causation and Finite Propagation Speed
• 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
• Modified Measures as an Effective Theory for Causal Fermion Systems
• On the Initial Value Problem for Causal Variational Principles
• The Chiral Index of the Fermionic Signature Operator
• Schroedinger vs. Navier-Stokes
• The Homogeneous Causal Action Principle on a Compact Domain in Momentum Space
• Dynamics of Causal Fermion Systems. Field Equations and Correction Terms for a New Unified Physical Theory
• Introduction to Causal Fermion Systems