Existence of minimizers for causal variational principles on compact subsets of momentum space in the homogeneous setting

@article{Langer2022ExistenceOM,
  title={Existence of minimizers for causal variational principles on compact subsets of momentum space in the homogeneous setting},
  author={Christoph Langer},
  journal={Calculus of Variations and Partial Differential Equations},
  year={2022}
}
  • Christoph Langer
  • Published 10 September 2021
  • Mathematics
  • Calculus of Variations and Partial Differential Equations
We prove the existence of minimizers for the causal action in the class of negative definite measures on compact subsets of momentum space in the homogeneous setting under several side conditions (constraints). The method is to employ Prohorov’s theorem. Given a minimizing sequence of negative definite measures, we show that, under suitable side conditions, a unitarily equivalent subsequence thereof is bounded. By restricting attention to compact subsets, from Prohorov’s theorem we deduce the… 
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The Homogeneous Causal Action Principle on a Compact Domain in Momentum Space
. The homogeneous causal action principle in a compact domain of momentum space is introduced. The connection to causal fermion systems is worked out. Existence and compactness results are reviewed.…

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