On the Structure of Minimizers of Causal Variational Principles in the Non-Compact and Equivariant Settings

Abstract

We derive the Euler-Lagrange equations for minimizers of causal variational principles in the non-compact setting with constraints, possibly prescribing symmetries. Considering first variations, we show that the minimizing measure is supported on the intersection of a hyperplane with a level set of a function which is homogeneous of degree two. Moreover, we perform second variations to obtain that the compact operator representing the quadratic part of the action is positive semi-definite. The key ingredient for the proof is a subtle adaptation of the Lagrange multiplier method to variational principles on convex sets.

24 pages, LaTeX, 2 figures, minor improvements (published version)

References in corpus (4)

• A Lorentzian Quantum Geometry
• Causal Fermion Systems: A Quantum Space-Time Emerging from an Action Principle
• On the Support of Minimizers of Causal Variational Principles
• An Action Principle for an Interacting Fermion System and its Analysis in the Continuum Limit

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• Fermionic Fock Spaces and Quantum States for Causal Fermion Systems
• Two-Dimensional Area and Matter Flux in the Theory of Causal Fermion Systems
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• A Notion of Entropy for Causal Fermion Systems
• A Canonical Construction of the Extended Hilbert Space for Causal Fermion Systems
• Introduction to Causal Fermion Systems
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