Causal Fermion Systems: Discrete Space-Times, Causation and Finite Propagation Speed

Abstract

The theory of causal fermion systems is a recent approach to fundamental physics. Giving quantum mechanics, general relativity and quantum field theory as limiting cases, it is a candidate for a unified physical theory. The dynamics is described by a novel variational principle, the so-called causal action principle. The causal action principle does not rely on a presupposed space-time structure. Instead, it is a variational principle for space-time itself as well as for all structures in space-time (like particles, fields, etc.). After a general motivation and introduction, we report on mathematical results for two-particle causal fermion systems which state that every minimizer describes a discrete space-time. We explain and make precise that on scales which are much larger than the scale of the microscopic space-time structures, the dynamics of a causal fermion system respects causality with a finite speed of propagation.

16 pages, LaTeX, 9 figures, notes of invited talk given at DICE2018, Castiglioncello, September 2018

References in corpus (3)

• A Hamiltonian Formulation of Causal Variational Principles
• Complex Structures on Jet Spaces and Bosonic Fock Space Dynamics for Causal Variational Principles
• The Causal Action in Minkowski Space and Surface Layer Integrals

Cited by in corpus (6)

• Causal Fermion Systems: An Elementary Introduction to Physical Ideas and Mathematical Concepts
• A Mechanism of Baryogenesis for Causal Fermion Systems
• Causal Fermion Systems and the ETH Approach to Quantum Theory
• Modified Measures as an Effective Theory for Causal Fermion Systems
• Models of Discrete Linear Evolution for Quantum Systems
• Linear Bosonic Quantum Field Theories Arising from Causal Variational Principles