On the Support of Minimizers of Causal Variational Principles

Abstract

A class of causal variational principles on a compact manifold is introduced and analyzed both numerically and analytically. It is proved under general assumptions that the support of a minimizing measure is either completely timelike, or it is singular in the sense that its interior is empty. In the examples of the circle, the sphere and certain flag manifolds, the general results are supplemented by a more detailed and explicit analysis of the minimizers. On the sphere, we get a connection to packing problems and the Tammes distribution. Moreover, the minimal action is estimated from above and below.

39 pages, LaTeX, 7 figures, introduction expanded, references added (published version)

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Cited by in corpus (20)

• Causal Fermion Systems: A Quantum Space-Time Emerging from an Action Principle
• A Hamiltonian Formulation of Causal Variational Principles
• Causal Fermion Systems: An Elementary Introduction to Physical Ideas and Mathematical Concepts
• On the Structure of Minimizers of Causal Variational Principles in the Non-Compact and Equivariant Settings
• Noether-Like Theorems for Causal Variational Principles
• Banach Manifold Structure and Infinite-Dimensional Analysis for Causal Fermion Systems
• The Causal Action in Minkowski Space and Surface Layer Integrals
• Spinors on Singular Spaces and the Topology of Causal Fermion Systems
• Causal Fermion Systems: Discrete Space-Times, Causation and Finite Propagation Speed
• A Class of Conserved Surface Layer Integrals for Causal Variational Principles
• Positive Functionals Induced by Minimizers of Causal Variational Principles
• Causal Variational Principles in the $\sigma$-Locally Compact Setting: Existence of Minimizers
• Causal Fermion Systems and the ETH Approach to Quantum Theory
• Singular Support of Minimizers of the Causal Variational Principle on the Sphere
• On the Initial Value Problem for Causal Variational Principles
• A Notion of Entropy for Causal Fermion Systems
• Potential theory with multivariate kernels
• Asymptotic properties of short-range interaction functionals
• Elliptic Methods for Solving the Linearized Field Equations of Causal Variational Principles
• A Positive Quasilocal Mass for Causal Variational Principles