Positive Functionals Induced by Minimizers of Causal Variational Principles

Considering second variations about a given minimizer of a causal variational principle, we derive positive functionals in space-time. It is shown that the strict positivity of these functionals ensures that the minimizer is nonlinearly stable within the class of compactly supported variations with local fragmentation. As applications, we endow the space of jets in space-time with Hilbert space structures and derive a positive surface layer integral on solutions of the linearized field equations.