Covariant conservation laws, local invariance and Noether's second theorem
General Relativity and Quantum Cosmology
2026-05-25 v3 High Energy Physics - Theory
Abstract
We lay down a set of requirements for a field theory to produce a covariant conservation law out of Noether's second theorem, and show that neither local invariance implies a covariant conservation law, nor the existence of a covariant conservation law necessarily stems from the local invariance of the theory. We illustrate our results with the examples of well-known theories.
Cite
@article{arxiv.2506.14454,
title = {Covariant conservation laws, local invariance and Noether's second theorem},
author = {Nuno Barros e Sá and Miguel A. S. Pinto and Tomás Trindade},
journal= {arXiv preprint arXiv:2506.14454},
year = {2026}
}
Comments
16 pages, accepted for publication in EPJC