The Linear Dynamics of Wave Functions in Causal Fermion Systems
arXiv:2101.08673 · doi:10.1016/j.jde.2021.05.025
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.
63 pages, LaTeX, 5 figures, minor improvements (published version)