Noether-like theorems for causal variational principles

The connection between symmetries and conservation laws as made by Noether’s theorem is extended to the context of causal variational principles and causal fermion systems. Different notions of continuous symmetries are introduced. It is proven that these symmetries give rise to corresponding conser...

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Bibliographic Details
Published in:Calculus of variations and partial differential equations Vol. 55; no. 2; pp. 1 - 41
Main Authors: Finster, Felix, Kleiner, Johannes
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.04.2016
Springer Nature B.V
Subjects:
Analysis
Calculus of Variations and Optimal Control; Optimization
Charge
Conservation
Conservation laws
Control
Energy conservation
Fermions
Mathematical analysis
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Minkowski space
Surface layers
Symmetry
Systems Theory
Theorems
Theoretical
Variational principles
49K21
49S05
58C35
58Z05
83C40
49K27
49Q20
ISSN:0944-2669, 1432-0835
Online Access:Get full text
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Summary:The connection between symmetries and conservation laws as made by Noether’s theorem is extended to the context of causal variational principles and causal fermion systems. Different notions of continuous symmetries are introduced. It is proven that these symmetries give rise to corresponding conserved quantities, expressed in terms of so-called surface layer integrals. In a suitable limiting case, the Noether-like theorems for causal fermion systems reproduce charge conservation and the conservation of energy and momentum in Minkowski space. Thus the conservation of charge and energy-momentum are found to be special cases of general conservation laws which are intrinsic to causal fermion systems.
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ISSN:0944-2669
1432-0835
DOI:10.1007/s00526-016-0966-y