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arXiv · 2506.14454

Covariant conservation laws, local invariance and Noether's second theorem

Nuno Barros e Sá·Miguel A. S. Pinto·Tomás Trindade
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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.

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Nuno Barros e Sá, Miguel A. S. Pinto, Tomás Trindade. 2025-06-17. Covariant conservation laws, local invariance and Noether's second theorem. https://arxiv.org/abs/2506.14454

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