Noether-like theorems for causal variational principles

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Abstract

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.

Mathematics Subject Classification

49Q20 49S05 58C35 58Z05 83C40 49K21 49K27 

Notes

Acknowledgments

J. K. gratefully acknowledges support by the “Studienstiftung des deutschen Volkes”.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Fakultät für MathematikUniversität RegensburgRegensburgGermany

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