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On the Structure of Minimizers of Causal Variational Principles in the Non-Compact and Equivariant Settings
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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.
Forward citations
Cited by 2 Pith papers
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Holographic Mixing and Fock Space Dynamics of Causal Fermion Systems
A limiting case of the causal action principle in causal fermion systems yields QED Fock space dynamics via stochastic fluctuating fields and dephasing, while introducing holographic mixing.
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Quantum Reference Frames and Correlation Geometry
Correlation geometry underlies causal fermion systems by providing a thermodynamic-style description of physical systems that incorporates gauge symmetries and diffeomorphisms via the principle of unitary equivalence.
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