  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.
