From Discrete Space-Time to Minkowski Space: Basic Mechanisms, Methods and Perspectives

Abstract

This survey article reviews recent results on fermion system in discrete space-time and corresponding systems in Minkowski space. After a basic introduction to the discrete setting, we explain a mechanism of spontaneous symmetry breaking which leads to the emergence of a discrete causal structure. As methods to study the transition between discrete space-time and Minkowski space, we describe a lattice model for a static and isotropic space-time, outline the analysis of regularization tails of vacuum Dirac sea configurations, and introduce a Lorentz invariant action for the masses of the Dirac seas. We mention the method of the continuum limit, which allows to analyze interacting systems. Open problems are discussed.

25 pages, LaTeX, 6 figures, minor improvements (published version)

References in corpus (3)

• An Action Principle for the Masses of Dirac Particles
• Fermion Systems in Discrete Space-Time Exemplifying the Spontaneous Generation of a Causal Structure
• A Lattice Model for the Fermionic Projector in a Static and Isotropic Space-Time

Cited by in corpus (7)

• A Lorentzian Quantum Geometry
• Causal Fermion Systems: A Quantum Space-Time Emerging from an Action Principle
• On the Support of Minimizers of Causal Variational Principles
• Entanglement and Second Quantization in the Framework of the Fermionic Projector
• An Action Principle for the Masses of Dirac Particles
• The Fermionic Projector, Entanglement, and the Collapse of the Wave Function
• The Causal Perturbation Expansion Revisited: Rescaling the Interacting Dirac Sea