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

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 defin...

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Bibliographic Details
Published in:Calculus of variations and partial differential equations Vol. 61; no. 4
Main Author: Langer, Christoph
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.08.2022
Springer Nature B.V
Subjects:
Analysis
Calculus of Variations and Optimal Control; Optimization
Control
Existence theorems
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Momentum
Systems Theory
Theoretical
Variational principles
49Jxx
28Cxx
ISSN:0944-2669, 1432-0835
Online Access:Get full text
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Summary: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 existence of minimizers in the class of negative definite measures.
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ISSN:0944-2669
1432-0835
DOI:10.1007/s00526-022-02233-4