Positive Functionals Induced by Minimizers of Causal Variational Principles

Abstract

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.

15 pages, LaTeX, 1 figure, minor improvements (published version)

References in corpus (2)

• A Hamiltonian Formulation of Causal Variational Principles
• The Causal Action in Minkowski Space and Surface Layer Integrals

Cited by in corpus (5)

• Complex Structures on Jet Spaces and Bosonic Fock Space Dynamics for Causal Variational Principles
• The Causal Action in Minkowski Space and Surface Layer Integrals
• Elliptic Methods for Solving the Linearized Field Equations of Causal Variational Principles
• A Canonical Construction of the Extended Hilbert Space for Causal Fermion Systems
• Holographic Mixing and Fock Space Dynamics of Causal Fermion Systems