The Linear Dynamics of Wave Functions in Causal Fermion Systems

Abstract

The dynamics of spinorial wave functions in a causal fermion system is studied. A so-called dynamical wave equation is derived. Its solutions form a Hilbert space, whose scalar product is represented by a conserved surface layer integral. We prove under general assumptions that the initial value problem for the dynamical wave equation admits a unique global solution. Causal Green's operators are constructed and analyzed. Our findings are illustrated in the example of the regularized Minkowski vacuum.

arXiv comment63 pages, LaTeX, 5 figures, minor improvements (published version)

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Cited by in corpus (10)

• Banach Manifold Structure and Infinite-Dimensional Analysis for Causal Fermion Systems
• Fermionic Fock Spaces and Quantum States for Causal Fermion Systems
• A Mechanism of Baryogenesis for Causal Fermion Systems
• Causal Fermion Systems as an Effective Collapse Theory
• A Notion of Entropy for Causal Fermion Systems
• A Mechanism for Dark Matter and Dark Energy in the Theory of Causal Fermion Systems
• Notions of Fermionic Entropies of a Causal Fermion System
• Linear Bosonic Quantum Field Theories Arising from Causal Variational Principles
• Holographic Mixing and Fock Space Dynamics of Causal Fermion Systems
• A Canonical Construction of the Extended Hilbert Space for Causal Fermion Systems