  Based on conservation laws for surface layer integrals for critical points of
causal variational principles, it is shown how jet spaces can be endowed with
an almost-complex structure. We analyze under which conditions the
almost-complex structure can be integrated to a canonical complex structure.
Combined with the scalar product expressed by a surface layer integral, we
obtain a complex Hilbert space $\mathfrak{h}$. The Euler-Lagrange equations of
the causal variational principle describe a nonlinear time evolution on
$\mathfrak{h}$. Rewriting multilinear operators on $\mathfrak{h}$ as linear
operators on corresponding tensor products and using a conservation law for a
nonlinear surface layer integral, we obtain a linear norm-preserving time
evolution on bosonic Fock spaces. The so-called holomorphic approximation is
introduced, in which the dynamics is described by a unitary time evolution on
the bosonic Fock space. The error of this approximation is quantified. Our
constructions explain why and under which assumptions critical points of causal
variational principles give rise to a second-quantized, unitary dynamics on
Fock spaces.
